Question

How do you differentiate `y=(x^2-4x)^3`?

Answer 1

`y'=6(x^2-4x)^2(x-2)`

Explanation:

Use the chain rule, which is basically "derivative of the outside times derivative of the inside":

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

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

Factor a 2 out of the last term to simplify:
`y'=3(x^2-4x)^2(2)(x-2)`

`y'=6(x^2-4x)^2(x-2)`