Question

Differentiate: $e^{\sin x}$

Answer 1

According to chain rule $\mathbf{f}\mathbf{\left(}\mathbf{g}\mathbf{\right(}\mathbf{x}\mathbf{\left)}\mathbf{\right)}\mathbf{=}{\mathbf{f}}^{\mathbf{\text{'}}}\mathbf{\left(}\mathbf{g}\mathbf{\right(}\mathbf{x}\mathbf{\left)}\mathbf{\right)}\mathbf{.}\mathbf{g}\mathbf{\text{'}}\mathbf{\left(}\mathbf{x}\mathbf{\right)}$

$$\begin{gathered} y=e^{\sin x} \\ \frac{dy}{dx}=e^{\sin x}\frac{d\sin x}{dx} \\ \frac{dy}{dx}=e^{\sin x}\cos x \end{gathered}$$

Hence, the differentiation $e^{\sin x}$ is ${\mathit{e}}^{\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{x}}\mathit{c}\mathit{o}\mathit{s}\mathit{x}$.