Question

Find the derivation of $\sin x^2+{\sin }^2{x}^2$.

Answer 1

Let,

$y=\sin x^2+{\sin }^2{x}^2$

$y=\sin x^2+{\left(\sin x^2\right)}^2$

Therefore,

$\frac{dy}{dx}=\cos x^2\times 2x+2\sin x^2\cos x^2\times 2x$

$\frac{dy}{dx}=2x\cos x^2(1+2\sin x^2)$

Hence, this is the required result.