A) \[\frac{1}{2\sqrt{x}}\]
B) \[\frac{{{\sec }^{2}}\sqrt{x}}{\sqrt{x}\tan x}\]
C) \[2{{\sec }^{2}}\sqrt{x}\]
D) \[\frac{{{\sec }^{2}}\sqrt{x}}{2\sqrt{x}\tan \sqrt{x}}\]
Correct Answer: D
Solution :
\[y=\log \tan \sqrt{x}\] \[\frac{dy}{dx}=\frac{1}{\tan \sqrt{x}}.{{\sec }^{2}}\sqrt{x}.\frac{1}{2\sqrt{x}}=\frac{{{\sec }^{2}}\sqrt{x}}{2\sqrt{x}\tan \sqrt{x}}\].
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