Question

Find the derivatives of the function:$f\left(x\right)=\sin \left(e^x\right).$

Short answer

The derivative of$f\left(x\right)=\sin \left(e^x\right)is\cos \left(e^x\right)\times e^x.$

Step-by-step solution

Given information 

The given expression is$f\left(x\right)=\sin \left(e^{\left(x\right)}\right).$

Simplification 

^{$$\begin{gathered} f\text{'}\left(x\right) \\ =\frac{d}{dx}\sin \left(e^x\right) \\ =\cos \left(e^x\right)\times \frac{d}{dx}\left(e^x\right) \\ =\cos \left(e^x\right)\times e^x \\ Hence,f\text{'}\left(x\right)=e^x\times \cos \left(e^x\right). \end{gathered}$$}