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

The correct answer is Option (3) → $-2x\cos(x^2)\sin(\sin(x^2))$

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

$\frac{dy}{dx}=-\sin(\sin x^2)\frac{d}{dx}(\sin x^2)$

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

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