Question

The derivative of $e^{\ln \left(\sin x\right)}$ with respect to $x$ where $x\in (0,\frac{\pi }{2}),$ is

[1 mark]

• A. $e^{\ln \left(\sin x\right)}\cdot \cos x$
• B. $\cos x$
• C. $e^{\sin x}$
• D. $e^{\cos x}$

Answer 1

The correct option is B $\cos x$

Let $y=e^{\ln \left(\sin x\right)}$
As we know $a^{{\log }_{a}m}=m,$
$\therefore y=\sin x$
Differentiating w.r.t. $x,$ we get
$\frac{dy}{dx}=\cos x$