# How do you find the derivative of sin(e^x)?

Apr 16, 2017

${e}^{x} \cos \left({e}^{x}\right)$

#### Explanation:

differentiate using the $\textcolor{b l u e}{\text{chain rule}}$

$\text{Given" f(x)=g(h(x))" then}$

• f'(x)=g'(h(x))xxh'(x)

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

$\Rightarrow f ' \left(x\right) = \cos \left({e}^{x}\right) \times \frac{d}{\mathrm{dx}} \left({e}^{x}\right)$

$\textcolor{w h i t e}{\Rightarrow f ' \left(x\right)} = {e}^{x} \cos \left({e}^{x}\right)$