Question

Let $y=\sqrt{\tan \sqrt{x}}$ then find $\frac{dy}{dx}$.

Answer 1

Given, $g=\sqrt{\tan \sqrt{x}}$

Now, $\frac{dy}{dx}=\frac{{\sec }^2\sqrt{x}}{2\sqrt{\tan \sqrt{x}}},\frac{1}{2\sqrt{x}}$

$=\frac{\left({\sec }^2\sqrt{x}\right)}{4\sqrt{x\tan \sqrt{x}}}$