Question

If $y=e^{\sin x}$, then find $\frac{dy}{dx}$

• A. $e^{\sin x}\cos x$
• B. $e^{\sin x}$
• C. $e^{\cos x}$
• D. $e^{\sin x\cos x}$

Answer 1

The correct option is A $e^{\sin x}\cos x$

Given,

$y=e^{\sin x}$

$\frac{dy}{dx}=\frac{d}{dx}{e}^{\sin x}$

$\frac{dy}{dx}=e^{\sin x}\frac{d}{dx}\sin x$.....................(applying chain rule of differentiation)

$\frac{dy}{dx}=e^{\sin x}\cos x$

Hence, the answer is option $A$