# How do you find the derivative of h(x)=f(x^2) using the chain rule?

Dec 23, 2015

#### Answer:

$h ' \left(x\right) = 2 x \cdot f ' \left({x}^{2}\right)$

#### Explanation:

According to the chain rule:

if $h \left(x\right) = f \left(g \left(x\right)\right)$, then

$h ' \left(x\right) = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$

In this case, $g \left(x\right) = {x}^{2}$ so

$h ' \left(x\right) = f ' \left({x}^{2}\right) \cdot \frac{d}{\mathrm{dx}} \left[{x}^{2}\right]$

$h ' \left(x\right) = 2 x \cdot f ' \left({x}^{2}\right)$
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