Question

Find $\frac{dy}{dx}$, if $y=\sqrt{1+\sin 2x}$.

Answer 1

$y=\sqrt{1+\sin 2x}$

We know that, $1={\sin }^{2}x+{\cos }^{2}x$ and $\sin 2x=2\sin x\cos x$

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

$y=\sqrt{(\sin x+\cos x{)}^2}$

$y=\sin x+\cos x$

Differentiating w.r.t $x$

$\frac{dy}{dx}=\cos x-\sin x$