Question

How do you implicitly differentiate `3y + y^4/x^2 = 2`?

Thanks for your help!

Answer 1

I found: `(dy)/(dx)=(2y^4)/(3x^3+4xy^3)`

Explanation:

ou need to remember to derive also `y` as a function of `x`, so, for example:
`y^2` derived will give you: `2y(dy)/(dx)`
in your case you get:
`3(dy)/(dx)+(4y^3x^2(dy)/(dx)-2xy^4)/x^4=0`
`3(dy)/(dx)+4y^3/x^2(dy)/(dx)-2y^4/x^3=0`
collect `(dy)/(dx)` and rearrange:
`(dy)/(dx)=(2y^4/x^3)/(3+4y^3/x^2)=(2y^4)/(3x^3+4xy^3)`

Answer 2

yes

Explanation:

me too when it was asked elsewhere

https://socratic.org/questions/how-do-you-implicitly-differentiate-3y-y-4-x-2-2-2#285710