Question

If$y=\cos (\sin x^2)$, then at $x=\sqrt{\frac{\mathrm{\pi }}{2}},\frac{dy}{dx}$ is equals to ?

• A. $-2$
• B. $2$
• C. $0$
• D. none of these

Answer 1

The correct option is C

$0$

Explanation for the correct option:

Find the value of $\frac{dy}{dx}$:

Given function,

$y=\cos (\sin x^2)$

Differentiate the given function with respect to $x$

$\frac{dy}{dx}=-\sin (\sin x^2).\cos x^2.2x\left[\because \frac{d\left(\cos x\right)}{dx}=-\sin x\right]$

Put value $x=\sqrt{\frac{\mathrm{\pi }}{2}}$ in obtained function:

$$\begin{gathered} \frac{dy}{dx}=-\sin (\sin \frac{\pi }{2}).\cos \left(\frac{\pi }{2}\right).2\sqrt{\frac{\mathrm{\pi }}{2}} \\ =0 \end{gathered}$$

Hence, the option (C) is correct.