Question

How do you find `dy/dx` by implicit differentiation of `x^3+y^3=8`?

Answer 1

`dy/dx=-x^2/y^2`

Explanation:

We have:

`x^3+y^3=8`

Differentiate wrt `x`; then Apply the chain rule (implicit differentiation):

`3x^2 + d/dxy^3=0`
`:. 3x^2 + dy/dxd/dyy^3=0`
`:. 3x^2 + dy/dx(3y^2)=0`
`:. x^2 + y^2dy/dx=0`
`:. dy/dx=-x^2/y^2`