Question

use implicit differentiation to find y' if x^3-xy+y^3=7

Answer 1

3x^2 - y - xy' + 3y^2y' = 0
Now solve for y'. Your answer will have x's and y's in it.

Answer 2

Mark do you understand how bang came up with those middle two terms?
It requires the product rule:\[\Large (-xy)'\quad=\quad -(x)'y-x(y)'\quad=\quad -(1)y-x(y')\]

Answer 3

Yeah, i think the product rule with implicit differentiation confuses a lot of people.

Answer 4

how do i get rid of the y' in the exponent

Answer 5

Hmm there are no y' in exponent positions.\[\Large (y^3)'\quad=\quad (3y^2)y'\]

Answer 6

I got it now i was reading it wrong before

Answer 7

Oh ok :)