# Question #22513

Oct 16, 2017

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

#### Explanation:

The derivative of ${e}^{x}$ is itself.

But since its $x$ has a function in it we apply the chain rule.
Where we take the derivative of the outside and then multiply it by the derivative of the inside.

Where ${e}^{\sin} x$ is our outside and $\sin x$ is our inside.

The derivative of $\sin x$ is $\cos x$

Put them together and you get:

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