find dy/dx by implicit differentiation?

Question

x^3 * y^3 -y = x

Answer 1

3x^2 + 3y^2*dy/dx - dy/dx = 1

(dy/dx)* (3y^2 -1) = 1 - 3x^2

dy/dx = [1 - 3x^2]/[3y^2 -1]

please check for errors.

Answer 2

Use product rule on x^3 y^3:

d/dx[x^3 y^3] = y^3 d/dx[x^3] + x^3 d/dx[y^3]
= y^3 3x^2 + x^3 3y^2 dy/dx

Then you have

y^3*3x^2 + x^3*3y^2*dy/dx - dy/dx = 1

Now, rearrange this so that all terms with dy/dx are on one side, and all other terms are on the other side. Then you can solve for dy/dx.

Answer 3

Implicit differentiation means all the variables are on one axes and it is given by (dy/dx)/x.
since, f(x)=x given
f'(x) =1 and implicit dy/dx=(dy/dx)/x=1/x

Answer 4

sorry.... i dont know