# How do you find the derivative of e^sinx?

May 25, 2018

$y ' = {e}^{\sin} \left(x\right) \cdot \cos \left(x\right)$

#### Explanation:

Taking the logarithm on both sides we get
$\ln \left(y\right) = \sin \left(x\right)$
Differentiating this with respect to $x$:
$\frac{1}{y} \cdot y ' = \cos \left(x\right)$
so
$y ' = {e}^{\sin \left(x\right)} \cdot \cos \left(x\right)$