Question

How do you differentiate `f(x)=(x^2-2x)^2` using the chain rule?

Answer 1

You can do it like this:

Explanation:

Treat the expression inside the brackets as a single function. Differentiate that, then multiply by the derivative of what you have inside the brackets:

`f(x)=(x^2-2x)^2`

So you let `(x^2-2x)=u`

So:

`dy/dx=(dy)/(cancel(du))xx(cancel(du))/(dx)`

`:.f'(x)=2(x^2-2x)^(1)xx(2x-2)`

This simplifies to:

`f'(x)=4x(x-1)(x-2)`