If y=e^ 1 2 (1+ ^2 x ) , then d y d x is equal to - Vidyadip

MCQ

If $y=e^{\frac{1}{2} \log \left(1+\tan ^2 x\right)}$, then $\frac{d y}{d x}$ is equal to

A
$\frac{1}{2} \sec ^2 x$
B
$\sec ^2 x$
✓
$\sec x \tan x$
D
$e^{\frac{1}{2} \log \left(1+\tan ^2 x\right)}$

✓

Answer

Correct option: C.

$\sec x \tan x$

$y=e^{\frac{1}{2} \log \left(1+\tan ^2 x\right)}=\left(\sec ^2 x\right)^{1 / 2}=\sec x$
$\therefore \frac{d y}{d x}=\sec x \tan x$

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