Question

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

Answer 1

$y=\sqrt{tanx}$

$y^2=tanx$

$2y\frac{dy}{dx}={\sec }^{2}x$

$\frac{dy}{dx}=\frac{{\sec }^{2}x}{2y}=\frac{{\sec }^{2}x}{2\sqrt{tanx}}$