Question

Differentiate the function $\sin \left(\cos x^2\right)$ with respect to $x$

Answer 1

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

Differentiate both side with respect to $x$.

$\frac{dy}{dx}$$=\frac{d\left\{\sin \cos x^2\right\}}{dx}$

= $\cos \left(\cos x^2\right)$$\frac{d}{dx}\left(\cos x^2\right)$

= $\cos \left(\cos x^2\right)$$\left(-\sin x^2\right)$$\frac{d}{dx}\left(x^2\right)$

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

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