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

Nov 30, 2015

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:

$f \left(x\right) = {\left({x}^{2} - 2 x\right)}^{2}$

So you let $\left({x}^{2} - 2 x\right) = u$

So:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\cancel{\mathrm{du}}} \times \frac{\cancel{\mathrm{du}}}{\mathrm{dx}}$

$\therefore f ' \left(x\right) = 2 {\left({x}^{2} - 2 x\right)}^{1} \times \left(2 x - 2\right)$

This simplifies to:

$f ' \left(x\right) = 4 x \left(x - 1\right) \left(x - 2\right)$