Answer
$4x \sin (x^2) \cos (x^2)$
Work Step by Step
Our aim is to solve the function $f(x)=\sin^2 (x^2)$
We differentiate both sides with respect to $x$.
$f^{\prime}(x)=\dfrac{d}{dx}[\sin^2 (x^2)]$
or, $=2 \sin^{(2-1)}(x^2) \dfrac{d}{dx} [ \sin^2 (x^2)]$
or, $=2 \sin (x^2)\cos (x^2) \times 2x$
or, $=4x \sin (x^2) \cos (x^2)$
