A community for students.
Here's the question you clicked on:
 0 viewing
malexander
 2 years ago
I am having trouble understanding the concept of implicit differentiation. Can anyone explain it in simple terms?
malexander
 2 years ago
I am having trouble understanding the concept of implicit differentiation. Can anyone explain it in simple terms?

This Question is Closed

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.21) differentiate left side 2) differentiate right side 3) isolate y' 4) substitute y (if possible)

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0can you give an example @lgbasallote ?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0simplest explanation i have ever seen is in the video here http://patrickjmt.com/ i cannot link directly to the video, but it is in the calculus section and very easy to understand

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2a good example would be \[y = a^x\] classic

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2note: a is a constant and x is the variable you wanna differentiate

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0i saw that same video @satellite73 . it was okayi tied to apply the same thing to a problem my professor gave me and i totally stalled :(

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0for example: ysinx+x^2y^2=2x

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2first term > use product rule second term > use product rule derivative of 2x would be 2

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0think "\(y=f(x), y'=f'(x)\) and use the product and chain rules where needed

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2product rule on ysin x would be... \[y(\cos x) + y' \sin x\] try product rule on second term

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2when i said second term i meant X^2 y^2

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0so..... dy/dx sinx+ycosx+2x2y=2?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2not exactly....you use power rule on x^2 y^2

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2*facepalm* product rule...darn these p's

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0so the product rule on x^2y^2 would be 2xy^2+x^2(dy/dx) ?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2not exactly...second term would be x^2 (2y)(dy/dx)

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2now combine all the info

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0wait...how is y^2 becoming 2y if your doing the product rule (f'g+fg')...

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2second term would be x^2 multipled to derivative of y^2 right?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2derivative of y^2 is 2y (dy/dx)

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0what im saying is that, if g(x) is y^2, the product rule calls for one of the g(x) not to become the g'(x)...so wouldnt one of the y^2 stay the same?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2y^2 stayed the same in 2xy^2

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2in the second term x^2 remains the same

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0im still not getting the concept (im a bit slow tonight, sorry)

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2by "second term" i am following your answer you said "so the product rule on x^2y^2 would be 2xy^2+x^2(dy/dx) ?"

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.22xy^2 is correct...you held y^2 constant then took the derivative of x^2 for the second term you held x^2 constant but took the derivative of y^2 wrong

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2derivative of y^2 is not simply dy/dx...it's 2y(dy/dx)

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0ohhhh okay! now i understand...so anytime you take the derivative of y...its not only its derivative but you put dy/dx at the end of it

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2that's pretty much it....so now combine all the info

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2i mean add the derivative of ysinx and the derivative of x^2y^2

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0so its: dy/dx sinx+ycosx+2xy^2+x^2 2y(dy/dx)=2

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2yep you got it...now bring to the right side all the terms that doesnt include dy/dx

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0sooo dy/dx sinx+x^2 2y(dy/dx)=2ycosx2xy^2 so far

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0so is it: dy/dx=2ycosx2xy^2/sinx+x^2 2y ?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.2yep...i dont suppose you can put y in terms of x so i guess that's the final answer...can you confirm @satellite73 ?

malexander
 2 years ago
Best ResponseYou've already chosen the best response.0NICEEE :D I never got this concept until now. Thanks so much for helping me out with this @lgbasallote . I will not close the question until @satellite73 responds to your query.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.