Question

Differentiate $\sqrt{\sin \sqrt{x}}$ w.r.t. $x$.

Answer 1

Let $y=$ $\sqrt{\sin \sqrt{x}}$.

Now differentiating both sides with respect to $x$ we get,

$\frac{dy}{dx}=\frac{\cos \sqrt{x}}{2\sqrt{\sin \sqrt{x}}.2\sqrt{x}}$

or, $\frac{dy}{dx}=\frac{\cos \sqrt{x}}{4\sqrt{\sin \sqrt{x}}\sqrt{x}}$