Derivative of $cos(sin(x)^2)$ with respect to x is:

$2xsin(x^2)cos(cos(x^2))$ $-2xsin(x^2)cos(cos(x^2))$ $-2xcos(x^2)sin(sin(x^2))$ $2xcos(x^2)sin(cos(x^2))$

$-2xcos(x^2)sin(sin(x^2))$

The correct answer is Option (3) → $-2x\cos(x^2)\sin(\sin(x^2))$ $y=\cos(\sin x^2)$ $\frac{dy}{dx}=-\sin(\sin x^2)\frac{d}{dx}(\sin x^2)$ $=-\sin(\sin x^2)\cos x^2\frac{d}{dx}x^2$ $=-2x\cos(x^2)\sin(\sin(x^2))$