Question

If $y=\log \tan \sqrt{x}$ then the value of $\frac{dy}{dx}$ is:

• A. $\frac{1}{2\sqrt{x}}$
• B. $\frac{{\sec }^2\sqrt{x}}{\sqrt{x}\tan x}$
• C. $2{\sec }^2\sqrt{x}$
• D. $\frac{{\sec }^2\sqrt{x}}{2\sqrt{x}\tan x}$

Answer 1

Answer: (D)

Let $y=\log \tan \sqrt{x}$
Diff. both side w.r.t 'x'
$\frac{dy}{dx}=\frac{1}{\tan \sqrt{x}}.\frac{d}{dx}\left(\tan \sqrt{x}\right)$
$=\frac{1}{\tan \sqrt{x}}.{\sec }^2\sqrt{x}.\frac{1}{2\sqrt{x}}$
$\Rightarrow \frac{dy}{dx}=\frac{1{\sec }^2\sqrt{x}}{2\sqrt{x}\tan \sqrt{x}}$