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

Apr 26, 2017

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

#### Explanation:

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

Use the chain rule to differentiate (derivative of the outside times derivative of the inside):

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

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