Differentiation Rules Lecture 2 | Implicit & Parametric Function Class 12 Maths | IIT JEE | Vedantu

Differentiation Rules Lecture 2 | Implicit & Parametric Function Class 12 Maths | IIT JEE | Vedantu



today's fast hello butcher how are you so this is our second class of differentiation and in the last class we just started differentiation which today classroom differentiation this start kita I'm the buccal basic concept some javac a differentiation hotaki how's the differentiation derived and just started differentiation by first principle take it in the meanwhile I saw some very nice discussion on invertible function happening in the chat guys we can do that discussion in the telegram group as well okay chello Oh Gabriel guys this is the classes of today which you must have attended electric potential by abhishek sir liquid solutions and differentiation is what we are doing now and now so guys the classes are happening on Monday Wednesday and Friday my math classes on differentiation right now we are covering differentiation right now and guys tomorrow and day after tomorrow are two classes so Saturday go we are doing graph transformation at 8:00 p.m. tomorrow okay this is under the course which I am taking all the functions and graphs so every week I am taking two classes on functions and graphs ticket that is on redness day and Saturday okay and I'm taking a short course on calculus Yahweh purpose care calculus cake holds my Mira to sort of be code calculus for you specially agar up class 11 through or in any case agar aapko calculus come meaningless imagine another when should I use integration when should I use differentiation its application and physics how should we visualize calculus is what I'm going to do here detailed course of integration I will do as we move ahead in these sequence of courses together how is wetness do come across nearly by the Pritam so that is this which I'm taking tomorrow okay but their success stories rukiruki happen so myth and sharad the videos are available on with anthos YouTube channel definitely watch them and one more thing guys all these Stoppers we are doing a talk show for you with them so there is a forum that has been circulated with you on the vedanta je channel and in the telegram group apples forum ethnic questions nick immediate ticket very soon we are doing a talk show with these guys taking your questions up cake questions jo a ticket voyons approaching it right cello and do like share and subscribe subscribe kuroh so that you keep getting the notifications and do like in the classes so that v teachers get to low key up touka-sama Gemara casa measure in the he ARA and this is the telegram group with where the discussions happen that this the link is also there in the description a link description maybe here her next to Reba Hannah Valley next story Sri ang will be off NVIDIA Nevada history of Perl inspire correctly Nvidia was actually not preparing for IIT Jade till class 12th who slit 12th my preparation start Kia and how did she clear kvp Y as well as Jay advanced with 600-something rank two skis to reapply caffeine's firing movie Hannah are given a budget a pariah this is what we are going to do we will start with first principle guys columnist some Java a quick revision now focus here now focus here quick revision column Nakata we studied that how a chord how accord converted into a tangent as the point Q started moving toward strangle his this point you started moving towards P Hannah Dominic Cod case local yeaa we started by taking the the slope of chord then we took the point x naught sorry point X shift towards X naught so as X tends to X naught the slope of chord converts into slope of the tangent or on the AV samjha key slope of the tangent to a curve is actually nothing but the slope of the tangent to a curve right is actually DV by DX that is actually divided by DX the slope of the tangent to the curve is actually dy by DX at that point so in those oh bugger combined current take again DeLuca combined during a two-carbon Jagga we will get the way to find out differentiation by what we call as the first principle differentiation by first principle right to em together so Jessica say points move Karthik are they are saying it so called as the point B keeps going towards a the slope of the the cod converts into the tangent the slope of the chord as X tends to X naught as X tends to X naught okay becomes what differentiation at the point X this is what we call as finding differentiation by first principle here the cochlea Jane advance this feeling bit of a question telegram to group a discus character have been hella it's a good question let us discuss that in the telegram group job future invertible hiking a function X equal to Y square you know when he got the move of function I can hear you be so sure is that a function at the first place each other anyways its kappa Roger now let's do the different let's do a few problems of how to differentiate using first principle this is important for your board examination this is important for your CBAC board examination understanding important hunk occurring a kissable function that differentiation the karna hoga FEV if we have to find the differentiation of any function what will you do we'll do our f of X plus h minus f of X upon H this is actually slope of the chord as H tends to 0 the cord becomes actually tangent and this becomes slope of the tangent or in the of derrive ability this is a right and derivative but right and derivative will be equal to the derivative because the the functions that we will be taking will be that variable functions as a function ski both carrying a just smooth graph of a jarppi sharp corner nahi hota so opera differentiation ho sakta the differentiation can happen there so if you do it by right hand the Riv ability or left hand deliverability does not matter ticket clear check the questions kirk addicted let's try to do a few questions will cool simpler let's start by differentiating y equal to X square by first principle of support ie but let's devote five minutes in doing practice of how to differentiate using first principle taken the sub Kohana but first principles of practice carrying it Javitch a eleventh or twelfth me this is important for the school examination take care soccer function get your function is f of X is equal to X square what did we learn we learned that differentiation dy by DX yeah f dash X can also be written as limit H tends to 0 by first principal f of X plus h minus f of X upon H what we have to do we have to simply put the values let's simply put the values Agger f of X X s square here then what will be f of X plus h if f of X is X square then f of X plus h guitar go in the place of X simply put X plus h f of X is X square f of X plus h is X plus h 2 whole square right so this can be written as limit H tends to 0 Kito Jagga X plus h K whole square minus f of X is X square upon H this is exactly what Newton in Lebanese actually derived when they thought about calculus for the very first time Jim Newton 11 its calculus cavalry my socha retina so this is how they first evolved the concept of limits so that is what limits is so important substantive limits concept in this samjha they sort of invented the concept of limits which led to the development of the entire branch of calculus ticket above Jack a Newton on Lebanon so Galle deceptive but they actually changed the way we look at the world around us right ticket H conservator last class of a pataga my name's Sudhir I take a H caserita when we started taking the poetry asada so there was a point X there was a point X plus h when we started taking this point towards X he beats me gap guitar HF and this point moves towards X then H tends to 0 maja say I 3 ticket so a guitar yeah Bob Solow perspective it's pretty simple to solve in you solve it now kilauea simply limit you know limit H tends to 0 X plus h go whole square is X square X square cancel oh jaga ticket you will be left with 2x h plus h square upon H ticket H or H cancel or jiying a your H and H will cancel this and this goes this goes but check akita this will tend to 0 this will become simply 2x you will get 2x and all of you anyways knew it sub capito key differentiation of X square is 2x but this is how you derive it right and similarly you can derive in the same way you can also derive differentiation of X square key J cap n be use curves like that you would have used n similar derivation would have given you you can try it on your own to do practice of to practice the questions of differentiation my first principle Rd Sharma's subjective case solved example Cardona bacio important for your school examination take it AJ click the important here but it is important for your school examination clear subbu clear a so similarly we can derive for any polynomial function right so what have you derived you derived two things you derived the differentiation of X square is 2x you also derived graphically a way to find slope of VY equal to X square happy grafica Kissimmee point capper tangent cash flow fine classic Tova right so if this is the graph of y equal to X square ha so qui upset which tire if somebody asks you in the graph of y equal to X square if there is a point X is equal to 2 if somebody wants to make a tangent to it right and if somebody asks you what is the slope of this tangent the slope of this tangent is nothing but the differentiation of the graph calculated at the point X is equal to 2 kita ziege other X equal to 2 pi y equal to X s square K graph by tangent plot karaage if you plot the tangent its slope is going to be 2 X when X is equal to 2 which is equal to actually 4 so what is the slope of this tangent for so differentiation graphically means slope of the tangent at any given point so much my recipe everybody clear with this yes or no Tigger habita a clue is asking sir is Caillou's coordinate geometry Malaika yes you can actually derive entire coordinate geometry entire tangent normal all the portions and also coordinate geometry may circle a la ellipse hyperbola sub coach actually differentiation say be correct a walk clear a cool algorithm now let's do two more problems of derivative by first principle just to practice sine X Kokoro Zara everybody do differentiation of sine X by first principle do it by first principle vaca physics Kings are up to reply neither Theo telegram permitted telegram K GroupMe macula you Mohawk sorry but J the purpose of that group is that all of you collaboratively learned together together for maybe beach beach Mansell Colorado tick yes derivation of Newton Lebanon sis you are right hi TJ Advanced aspirin TS you are right Newton lipids vicar amiable the last class of my differentiation will be on Newton the minutes take a solo career huh so if X is equal to sine X a block arrow up coconut up go find can i f dash X by first principle you will say limit H tends to 0 f of X plus h minus f of X upon H simply keep putting the values simply keep putting the values cows anagha capacity limit H tends to 0 f of X plus h I got a f of X sine X f if f of X is sine X then f of X plus h will be replace X by X plus h replace X by X plus h to get hours I got sine of X plus h minus sine X upon H right now what will happen sine C minus sine D all of you know what is sine C minus sine D sine C minus sine D katate 2 sine C minus D by 2 cos C plus D by 2 right yes or no sine C minus D by 2 cos C plus D by 2 Carlo so limit H tends to 0 Kilauea sign C minus D by 2 X plus h minus X X cancel ooga Kito jaga H by 2 yes Hanna fit freaky Tom jogger cause of this Plus this car luganskaya right should I show you the calculations let's see the calculations they glow yeah formulas sine C minus sine dica rockne use kiya kiya basket Agha C minus D by 2 H by 2 then cos this Plus this by 2 2 X plus h by 2 aziah upon H by to create curly ma why did we create a chai 2 because this will tend to one sign something buy something take a sign something by that something tends to one so I try to create connect Lehmann 1/2 say take care so how to and to create Katya right so yeah Thor tends to one okay this tends to 1 this is not indeterminate simply put H equal to 0 you get those like a Cossacks to say to cancel or Agha you will be simply left with Cossacks you will be simply left with Cossacks right clear a sociopath is sine X carefrontation is cos x nothing nothing special so this is the fundamental method to do differentiation this is called as differentiation by first principle up keyboard-based equations eyeing it in board you will get the question to differentiate say sine x by first principle I mean first principle key questions clearly somebody is asking Caputo ha first principle board carry important a beta tenth class cos Sudhir I there is a separate with an to channel for 9th and 10th so with search for vid on to 9th and 10th there is a separate channel for with on to 9th and 10th up in the in throat any classes oathean right of OB at intersect there are given in Chaves special hobbies cooker there let's do derivative of e race for 2 X by 3 2 X plus 3 by first principle last question on the first principle Farah keyboarding it soak a different shade can I ever fix is given to you as erased 2 power 2 X plus 3 we have to differentiate this by first principle do it hi a thought of boring principal a beta or the theory but this is what it is Joe here so here all right I use data yeah this we are not a replacing differentiation by this this is a new this is a method ha we must set timetable Gujral so every day there are classes from 4 to 7 p.m. and there are extra there are other courses which keep happening on other times so 12 key classes ot up key monday wetness day and Friday on the other days there are 11th classes and there are separate courses for example on Sunday I am taking calculus course ticket and on the witness day and Saturday I'm taking functions and graphs car course tick ok buddy huh so first principles I guess agreeing is go limit F dash X cut offered offered this is a problem of limits it's a problem of limits so limit H tends to 0 f of X plus h minus f of X upon H putting the value we are going to get limit H tends to 0 e raise to power now X plus h in the place of X you will get X plus h e raised to power 2 times X plus h plus 3 minus f of X which is e raised to power yeah this is what will come together Clearasil you the answer there go here is 2 power 2 X plus 3 those are my Commodus attack can you take out erased about 2x plus 3 common he raised to power 2x plus 3 can you take that common right this is cop Cassidy destructive you can read this as e raised to power 2 X + 3 + H can be read as he raised to power 2 X + 3 into e raised forage superior anybody in it out in this Hannah he raised to power a in – sorry he raised to power a plus V cotton but that would be a success but but chicken fuse was out there a bit that's why I'm just putting it right so this can be written like this here is part 2 X + 3 into arrays for it sorry – it's my right to H to H a together so ESCOs are commonly lo que Haga this can be written as this can be written as limit H tends to 0 e raised to power 2 X + 3 I'm taking common but check agita ya habiba ja e raised to power 2 H minus 1 upon H do you see this are a problem solved problem to solve oh yeah q q keep this so you know he raised to power something minus 1 upon something meth lab to deduce though can I give two here so I raise to power something minus 1 upon something as something tends to 0 right becomes 1 Q key to say up a multi divided katha so I have to multiply 2 as well right so this thing is tending to 0 but chiquita simply put a CH bus back either couch indeterminate Haney so simply get out jogger 2 times e raised to power 2 X + 3 which is your answer which is our answer degree segovia so these are the problems of limits actually the problems of differentiation by first principle are actually problems of limits or the problems of derivable et voilá chapter a givethem tick done forgiven I have solved it for you as well notes mil jag app Co you will get all this in the notes ticker the PDF of my classes or all the Vedanta classes are available in the description of each class or you can also get them through a pure salt caramel every cleaner you can also get them where in the weight onto app you can download with onto a Mohammed email jagoff CO and we also share the PDF of all the classes in the telegram group app telegram group maybe Jackie the extractive ticket clearance of Kwai Chung okay birthday now up the other time these devote car they took a basic formulas of course all of you know the basic family let me just revise the basic formula right so all of you know the basic formula k basic formula with the differentiation k but now you know how are these derived how are all these derived all these are derived by first principle right source of capital x-rays paren car differentiation is NX ki power n minus one all of you know similarly X cube cut 3x squared 1 upon X akitaka minus 1 upon X square you know P recipe you have to give anybody knows looked out similarly you know the formula of logarithmic and exponential functions all of you know this Quixote by chain rule of occurring a chain rule habit chain was getting a better together so all differentiation formal ever derived how here's some Newton 11 it's good time to derive key they aluminum ticket so they derived all these differentiation and integral calculus this was the method first principle was the method he and loot Carlos sorry formulas of coup pathology here you know I say you happy important to by the way these are important either Correa gained autonomy choco threesome kupatana it D by DX of e keep our exclusive capita it does not change it does not change right but if somebody wants you to differentiate d by DX of e raised to power X tocadisco through differentiation without upper a raise to power X Ln a it becomes a raised to power X Ln a right we will do it after some time arrear g talks Q 2 logs ever the CF not fun delegate era to answer from chain rule is different from Laurel method Cuba why are you scolding mathematics mathematics is mathematics it is true though result near thing yeah I thought the method another okay now similarly and then I cut out D by DX of n Linux mclubbe log to the base he always remember base today he can you a formula from the Pollack's died but if the base is not e if the base is not e tokyo jaga you have a mistake are thing d by DX of log X to the base a what will you do you will first change the base sub base changing property by that loci log to the base B can also be written as log a upon law of B whatever base that you want to put you can put whatever base that you want to put say C this is what we call as the base changing property right so it's coming across it down what I can do here this can be written as using this base changing property D by DX of based without ya he let me take the basis e log X to the base e upon so log X upon logging upon log a butt to the base e Hanna log X to the base is log X upon log a basically a minute he Lydia right so this is a constant this is a constant constant can be taken out of the differentiation so this becomes 1 upon log a to the base e into D by DX off now log X to the base E which is olynyk's in a log natural Yukito Jagga Virna Pollock's he will check up on the products giving you the answer giving you the answer this Verna products guitar answer answer logic of 1 upon X and then a 1 upon X Ln a he f ed log a to the base e tohoku pulled a jockey will accept there this property also everybody knows write one more property log a to the base B can also be written as 1 upon log B to the base a so either you write log a to the base e in the denominator or you write log e to the base in the numerator both are same yes or no clear is appear very basics see differentiation is very simple so I have to focus on the basics here Q key Bucky Jesus simple Lee Curtis candle Hannah how because you can do this in this is xi xi vb up Servius are each is there anything up code take any I'll give it now let's move on these are the output path I so I'm not waste time here all of you know this I will just put it out nothing special he started formally I've gotta sign the cause Koska minus sign 10 cos secant square cot come minus cosecant square secant cosecant X 10 X take care cosecant become minus cosecant cot right and you also know the differentiation of inverse trigonometric functions what are the differentiation of inverse trigonometric functions these are these tickets are up the load swivel diagram you will get all these in the notes hmm guys can you see me I just messaged you on the chat as well right Joel oh cool cool cool we are back ha so guys what we were doing so we just saw the formula for the inverse trigonometric differentiation right now what we'll do let's move it so you have observe we will not waste time now so we will now focus on the problem solving you keep basics everybody knows all of you know that when you add two functions then and then differentiate differentiate addition or subtraction of two functions it is as good as differentiate the individual function and then add or subtract Hisoka path ie right nothing is special about it similarly all of you know that if you multiply a constant with a function and differentiate the constant comes out of the differentiation nothing is special there is nothing special here so let's move ahead and solve some problems quickly for practice do it these are like Bill cool but chair level problems but still for the sake of practice please do it for the sake of practice please do it Team X again can you come here in the meanwhile how about chocolate Carrasco take second ha quickly Eliot something on there follow phew ready cello near Osaka Pattaya this is 2x Cossacks guitar I got minus 2 upon X cube Nikita Yaga very simple you can write this as a X raised to power 2 minus 1/2 that is 3 by 2 plus B X raised to power half plus CX R is 4 minus 1/2 right and now differentiate right many's the root X plus of Kasich combined kardea so it looks pretty simple differentiation psychopaths ahiki taja 3 by 2 n X raised to power a constant comes outside 3 by 2 x-rays forget how jaga 3 by 2 minus 1 that is 1 by 2 take a plus B by 2 B constant 1/2 outside x-rays 4 1 by 2 minus 1 XT power minus half or yukitoshi a minus C by 2 minus half minus 1 minus 3 by 2 upon X 2 is 4 3 by 2 I know pretty simple all of you know this nothing special here similarly you can solve that as well right answers checked earlier this is I'm just giving you for practice nothing special nothing new here it is just for your practice you can check the answers I give adding is give up so the thing is you should not do any calculation mistake at this level that's it nothing is special cool could you turn it the other Kevin it did I do something else minute subtract each again I did the other care how the calculation was take math kana if I was doing some calculation mistake PK when I was a viewer age many life make calculation mistake was like the big problem I used to do lots of calculation mistakes one thing that I learnt and I want I want to tell you but that calculation mistake table Athiya typically when what you are writing you not rather than concentrating on it your brain is moving a step further typically Marisa the problem OCD metalic Rehana was time to my egg to step august social other so then learnt with time that whenever I used to write something quickly for a fraction of second I used to look at it and think ah kaki a minute ah okay and then I used to move ahead because it's a super duper problem calculation mistake since in the mistakes is a big big problem Hannah and I used to be like super trouble with that ha oh yeah of course of coefficient ruler product will be put that nothing special here Hannah FX into GX first function the differentiation second function then second function differentiation into first function nothing special quotient rule denominator into differentiation of numerator minus numerator into differentiation of denominator upon denominator cos square nothing is special here let's simply solve problems for Taffet Kuro in fact is smitten kneecap where they are given X I next dose of local Dogon X sine X some local okay it is X cos plus cos into 1 right so differentiation of X in to sine X plus difference with X into differentiation of sine X right so it becomes 1 into sine X plus X into cos x nothing is special here I am going a bit fast because all of you know all this stuff it's cocoros are up quickly do it very very fast 7x keep our 3 by 2 into cos x just write it down quickly this write it down quickly for a – Niaga kiss them – like a thumb up a+ i his Coleco sarasu 7x keep our 3 by 2 into cos x ha dying isn't lee Jang but to jiying it covertly curlew do it with your hand nothing wrong in doing some practice ha cow saga first you will differentiate X key power 3 by 2 which is 3 by 2 X raise to power half into cos x + toska differentiation was like a minus sign into X key power 3 by 2 7 is common outside right 3 an surrogate answer this is answered you can check 7xt power half into 3 by 2 cos x minus 7 into X raise to power 3 by 2 into sine X clear this is the answer I hope it's clear to all of you ticket show the very nice very good hockey but Thais a ha I mean skew barrage now let's do this now if now down let's do this when three functions are getting multiplied what do you do what do you do Nene Whitlock is everything a sarthak we don't use log right now eyeing your skipper where should we use log I'll teach that don't worry logarithmic differentiation carrying it but you have to Co is there nothing here what is this it is multiplication of three functions two ways of doing it but finally we'll talk about a shortcut here other is for differentiate can I so take the recap okay break it into two parts break into two parts aka low say X cube eight lilo IRA's to power X sine X here sine X I by the way is sine keep our X needed sine X right now we can treat this as first function into second function right to get our table below game is scary frenzied ation that is three X square into differentiation of into simply erased to power X sine X right Plus do sahajayoga X cube as it is X cube as it is and differentiation of e raised to power X sine X agree yeah ethic ducati need to solve okay now you will apply product rule here so this will convert into this will convert into 3x square into e raised to power X sine X plus this as it is right is skander guitar I got X cube into e raised for extra differentiation like power ear is 4 X sine X plus excu dirige Pollux as it is now sinx car differentiation which is cossacks this is the answer right now if you look at it very very carefully what you are seeing here is sub sepilok our if you see it very very carefully there are three terms which come in the first term apke X cubed differentiation again in the first term the first function got differentiated in the second term actually your second function got differentiated Bakke as it is Bucky as it is in the third term in the third term your third function got differentiated Bucky sub couch as it is so whenever you get whenever you get multiplication of multiple functions and you want to differentiate that together you wish X again beta X I so up Kukoc and I you write all these different different terms or hurrican the ache ache ache ache function but differentiate curvature a job right he is sign keep our X theta whatever sign X term so gel that was sine x naught sine keep our X take care whose skin is logarithmic differentiation is sine X keep our X Jogja Boubacar nasty conga that will be logarithmic differentiation so what we just talked about so we talked about if there are three functions come multiplication or multiple functions come multiplication we keep multiple differentiating each function one by one so his characterization without higher its differentiation will be subsequently is could differentiate column and X raise to power n minus 1 I differentiated the first one the rest two residues Plus now we will differentiate the second term rest as it is X keep our n as it is taken into blockage to the base a a be kept upon the log X to the basic in tauranga run upon X Ln E this is it is plus now we will differentiate the third one the rest to as it is took at Osaka X raise to power n log X to the base a iki power extra differentiation Iggy power X itself this is your answer got it this is your answer clearly please you go down Tony Iskander anybody any doubt in this anybody need out high equal away array or t-shirt any merry passage very kooky t-shirt kind of obviously Yama Kira I give her their each other let's move it three up cancers no no problem here now our Utica question tool all of you know the quotient rule right so 10x cut differentiation Agoura Punk array using quotient rule Tokyo jaga it is subtly keep denominator as it is denominator differentiation of numerator minus numerator differentiate differentiation of denominator upon denominator cos square to Kitaj I got tossed into cos minus sign into minus sign right so jaga upon cos corrects that is cos 4x plus sine square X upon cos square X cos 4x plus sine square X without a given one upon cos square X which is secant square X so differentiation of tan X is secant square X which you already know nothing special here's push beta what is your doubt there is van what's your doubt ha tell me the doubts if this was all of you knew this one just skipping it I mean I'm just going very fast you gave up already Kerchak yo till class 11 than 12 both together ha hee Carlos all just do it quickly mysterious what should out beta cake bar the roots a device crew from the replay if you have any doubt you can ask in the telegram group as well mysterious last question we can doubt that it was simply application of quotient rule you have a piece of a piece of occurring ebon will again do the same thing ha telegram open Utah quibble right would you can network network say try guru don't use geo Network this week a guru gap for sine X upon 2 plus cos x sub separately karaage you will keep the denominator first as it is and you will differentiate the numerator so d by DX of the numerator denominator differentiation of numerator minus numerator into differentiation of denominator upon denominator square the rest is simple calculation Prologo 2x plus cos x as it is for sine x cut differentiation for cos x minus 4 sine x as it is 2 plus 2x plus cost extra differentiation 2x car to Koska minus sign upon 2x plus cos x car whole square right then less this simplification the rest is simplification hello so can see rajagaha this is the answer this is dance whatever it is this is the answer ha you can look at of it do it this one last question miss square Q Cara satyam read denominator cos square beta denominator cos square numerator into differentiation of numerator to vieira micaiah upon denominator cos square ha yoga this part is click it again step 1 what is the step one this so karaage denominator free say Jessica formula made out to the air this is denominator into differentiation of numerator minus numerator into differentiation of denominator agree upon denominator cap whole square this is the formula this is the formula right take care so I guess all the way through cuyahoga when you solve it further when you will solve it further what will you get here is 4x plus 0 is 4 minus X as it is here is 4x clear differentiation IRA's perixx erased / – second differentiation without that the aquatic law of calculation dick low answer like without fish and younger so erase one – extra differentiation now this is like general skipper Ryan gave me this is like erased for minus X Sena so he raised to power minus X then minus XK deterrence issues like minus sign be Uyghur right so erased bar minus X characterization is – time series for minus X right so it's a differentiation guitar jaga – variety + oh yeah he raised to power minus 6 minus similarly e raise power X minus X erased / – extra differentiation ho jaga – times e raised to power minus X solve kiya up capacity on Sarah Jane yeah anybody any doubt clear anybody any doubt in this if you're in class 11 then haven't done it properly then generic calculus cuckolded so rahama pace up or detail back around ah take it but if you're in class 12th and droppers two years of gzip melodies like super simple for you nothing special here right now let us simply do chain rule and in the class today Oriana are giving it so this is the chain rule guys so the chain rule says this if you have a function if you have a function like y is equal to G of H of K of X right then how do we differentiate then how do we find dy by DX is the question right so this is the question this is what we call this chain rule brijesh rate of formula like have our formula job PDF Milligan ah was mr. a formula okay so don't worry so don't worry about that now it's good to finish it classically how do we differentiate it it's a differentiation you're thorough job when we differentiate dy by DX na so dy by DX actually no time basically sub similar fiato you first differentiate the outermost function you first differentiate the outermost function that is G – G – under you will decay as it is may be example go through explain guru ha then escape bathwater function H – under Jubilee kya as it is in to K dash X ticket akk k– Gurkha differentiate cottage other best is to understand it with an example Jess a manga question they they D by DX off let me take an example separately right he explained Kiev I but may have two examples explained although it does a good complicated kindig easier with name let me explain it with you an example say applica differentiate can i d by DX of sign of log of ticket man they take woohyuk function or a little say upon the little lock in the Khalid save on the little kha'zix ticket sign off log of Cossacks sub similar cases so show in your mind just read it like this it has written sign of something sign of something sign of something a differentiation without the achoo sign of something cut differentiation Vltava cost of something to his concert guitars I got cause of something right so sign subsea panic is what is initiate karaage outermost function go sign something cut differentiation guitars like a cause of jobina Kavitha jubilee Kawada sign something a differentiation cause something and what is that something that is log of course X into don't stop there now what will you differentiate log off something now you differentiate log of something log of something the Vltava chose log of something at a filling station without to the base here to the base here okay log car differentiation without on run upon log X characterizations 1 upon X log something a differentiation run upon something right tiki-taka this should be 1 upon 1 upon juvie lik have attained Kelly quwata it was written as cos x into shouldn't Jose last with something forever there's something which is there in the last of it Scooby differentiate Caro Costco differentiation without a minus sign so much higher this is very simple it is very simple so this chain rule Carrollton sign something that differentiation cause something logs can direct the lock or differentiation Verna pond filled liquor cause Costco differentiation minus sign very simple nothing special about it take it how are they push mahir 11 to be kirinda here yeah you have to do it in 11th he will not be able to do physics without this take so much my anybody need out in this he is subcritical I squeezed a Rodney no need to go here but when I have Kelly sub Theory the creek here but it looks complicated simply got a sign of log for the differentiation of sign of log Delhi Savitha chain rule y is equal to sine of taken what is dy by DX gentleman say sign something into log substep Atticus could officiate karaage subsequently score differentiate karaage sign of something sign of something cut out jaga cause of some thing ticket katha or something what was that something something was long Shalaby came at me in to log log differentiation guitar jaga 1 upon X exceed potentially Neil this is the answer answer is toss of log X into other projects take a course of log expose Chandra there on the celica Chandra send them in all of your right he can push so much Michael TK Kiev name cause case at law geiger cause something into log X car differentiation clearly Zupko ticket whose counsel ki Jaya this is the answer subsidized sign could arrange it here cause so yeah Phil Laak would differentiate here for the politics oh yeah toss lnx when the Pollack's is Kokoro serra do it do this one after that I'm going to give you some home assignments today I'm going to give you some home assignments Mahmoud Muslim mill what should out did I miss your doubt somewhere ha sign off something in to e raise to power something the cones are katha so uh nog is saying DS dancer ashish is asking son next success story kawaiguy I think next three foot is Margherita mistress is asking clearly obviously arrow jaga publicly record then they go kalakeya huh me differentiate can write D by DX of sign off erased to power of X square plus 3 X minus 2 casa pouring is go read it with me it is written sign of something sign something called differenciate curve sign of something a differentiation yoga sign of something at a filling station guitar I go sign cacao saga cause just something else quite sick is it's for the x multiplied by multiplying now under kazakh what will come inside as it is erased to power ana sign something sign the ba is equal to cos the buff sign into something car differences sorry sign of something differentiation cause of something now II keep our something now read it like this how will you read it II keep our something what is the differentiation of e keep our something cut differentiation without that he keep our something of Papa's say I keep our something or that he keep our something is you keep over something in differentiation to Iquitos agar multiplying 2 cos Omega multiplied by E raised to power some thing as I got any doubt any doubt but what is that something what is that something written up multiplied so this into this but are you / veto something like how I eat keep our something may go with or something here is something I've got differentiation over now differentiate this not differentiation of this something book a thousand I got into differentiation of that Bogota jaga Kuro X is square cut 2 X + 3 constant of 0 ziege this is the answer so what is the answer answer is cos of this into e keep our this in – 2 X + 3 sahaja yoga now so it's cancer ayah this is cos of erased to power X square plus 3 X minus 2 multiplied by E raised to power X square plus 3 X minus 2 x – x + 3 now question is at X equal to 1 Kooskia when you find connieyc at X is equal to 1 is 4 again that put X equal to 1 just substitute X equal to 1 here keeta yaga yaga cause off he raised to power 1 Paquita 1 – 2 3 3 plus 1 minus 2 into 3 plus 1 minus 2 into this to be a clear answer Catania ara anybody need out in this guy's anybody need out Hopkins sahaja yoga a 5 e square cos e square clear each other damn now there are some home assignment problems that I'm giving you you can solve this just take a snapshot a snapshot of this and solve it very simple one house and I take your suggestion ha yeah Nokia is sub concert when I put DIY now note this one this is another another problem you can take it from the video because next class cut time or I am stretching it this is the next problem that I want you to solve this is J 2013 problem but very simple J 2030 problem but very simple take this one together you can take a snapshot you can give me the answer in the comments just give the answer in the comments ok give the answer in the comments this is another problem second assignment problem together and third one is this one this is tricky one yep naa trippin yo thathe ya take a snapshot let's see who can solve it let's see who can solve it this is a very nice problem let's see you can solve this one spatially 12 students and droppers haha sheesh testes who give it up there will be tests Ares don't worry yay karna and I'm just closing the class after this my dive two classes coming up tomorrow 8:00 p.m. transformation of graph graph transformation tomorrow 8:00 p.m. and Sunday go there is a class on calculus that classroom calculus is majorly for 11th graders to help you understand calculus in detail together that is the class for typically 11th graders well cool Shirou says start getting a what is calculus how to visualize it how to do differentiation from the basics and integration take care cello let's finish of the class I want to see the answer in the comment box come into box which cancels in a year try question and let's see who can solve this one okay bye bye see you tomorrow at 8 p.m. and then on Sunday and then on Monday in differentiation 3 tick each other okay Baba I see you be happy and keep smiling always y equal to X square by

23 thoughts on “Differentiation Rules Lecture 2 | Implicit & Parametric Function Class 12 Maths | IIT JEE | Vedantu

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  2. Thank you so much sir.🙏🙏
    After watching your lectures on continuity I look at the example problems and I was able to solve it without looking at the solutions and this really built my confidence to face tougher problems.

  3. last answer is c
    Take y =x^2 or y=x^3 and then
    check it for all the answers
    >>>The other ans are
    -2/3
    1/root2

  4. Last question d^2x/dy^2 >>>> option d
    Solution ,taking sir's favourite eq y=x^2
    And clever substitution will lead to the ans

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