Question

If $y=\cos \left(\sin x^2\right),$ then at $x=\sqrt{\frac{\pi }{2},}$ Find $\frac{dy}{dx}$

• A. $-2$
• B. $2$
• C. $-2\sqrt{\frac{\pi }{2}}$
• D. $0$

Answer 1

The correct option is D $0$

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

Now, $\frac{dy}{dx}=-\sin \left(sin{x}^2\right).\cos x^2.2x$

Now at $x=\sqrt{\frac{\pi }{2}}$

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