Question

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

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

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 }(\tan \sqrt{ x }) $
$=\frac{1}{\tan \sqrt{ x }} .\sec ^{2} \sqrt{ x } .\frac{1}{2 \sqrt{ x }}$
$ \Rightarrow \frac{ dy }{ dx }=\frac{1 \sec ^{2} \sqrt{ x }}{2 \sqrt{ x } \tan \sqrt{ x }}$