Question:

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

Updated On: Jul 6, 2022
  • $\frac{1}{2\sqrt{x}}$
  • $\frac{\sec^{2} \sqrt{x}}{\sqrt{x} \tan x}$
  • $2 \, \sec^2 \sqrt{x}$
  • $\frac{\sec^{2} \sqrt{x}}{2\sqrt{x} \tan x}$
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The Correct Option is D

Solution and Explanation

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