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  4. If y=e(1/2)log(1+tan2 x), then (dy/dx) is equal to

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

Continuity and Differentiability

Solution:

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