Q. If $y = e^{\frac{1}{2}\log{(1 + \tan^{2}{x)}}},\ then\frac{dy}{dx}$ is equal to
A) $\frac{1}{2}\sec^{2}x$
B) $\sec^{2}x$
C) $\sec{x\ \tan\ x}$
D) $e^{\frac{1}{2}\log{(1 + \tan^{2}{x)}}}$
Explanation
(c)
$\because y = e^{\frac{1}{2}\log{(1 + \tan^{2}{x)}}}$
$= ({\sec^{2}{x)}}^{1/2} = \sec x$
$\therefore\frac{dy}{dx} = \sec{x\tan x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.