derivative questions??

Question

what is the derivative of this?

y(x^3) -2(y^2)x=4

Answer 1

[ y'(x^3) + y(3x^2) ] - [ 4y*y'x + 2y^2 ] = 0
Then solve by isolating for y'

Basically, use the product rule

[ y'(x^3) + y(3x^2) ] - [ 4y*y'x + 2y^2 ] = 0
y'(x^3) + y(3x^2) - 4y*y'x - 2y^2 = 0
y'(x^3) - 4y*y'x = -y(3x^2) +2y^2
y' (x^3 -4yx) =-y(3x^2) +2y^2
y' = [-y(3x^2) +2y^2] / (x^3 -4yx)

Answer 2

It's actually:

use the product rule.

-y*3x^2+2y^2 / x^3 +4yx = y'

This is the correct answer.