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

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

$y=\sin(\cos(x^2))$,  $z=x^2$

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

$\frac{dz}{dx}=2x$

$⇒\frac{dy}{dz}=-\cos (\cos(x^2))\sin(x^2)$