Question

what is the derivative of e^sinex^1/2 by chain rule.

Answer 1

$$\begin{gathered} \frac{d}{dx}{e}^{\sin x}\sqrt{x} \\ U\sin gproductrule, \\ =\sqrt{x}\frac{d}{dx}{e}^{\sin x}+e^{\sin x}\frac{d}{dx}\sqrt{x} \\ U\sin gchainrulewehave \\ \frac{d}{dx}{e}^{\sin x}=\frac{d{e}^u}{du}\frac{d\sin x}{dx}=e^u\cos x=e^{\sin x}\cos x \\ Sowehave \\ =\sqrt{x}{e}^{\sin x}\cos x+e^{\sin x}\frac{1}{2\sqrt{x}} \\ =e^{\sin x}(\sqrt{x}\cos x+\frac{1}{2\sqrt{x}})Ans \end{gathered}$$