Question

Derivative of $\log (\sec \theta +\tan \theta )$ with respect to $\sec \theta$ at $\theta =\frac{\pi }{4}$ is ...........

• A. $0$
• B. $1$
• C. $\frac{1}{\sqrt{2}}$
• D. $\sqrt{2}$

Answer 1

The correct option is B $1$

$\frac{dg}{df}=\frac{dg}{dx}.\frac{dx}{df}=\frac{\frac{dg}{dx}}{\frac{df}{dx}}=\frac{g^{\prime }x}{f^{\prime }x}$

$\frac{d\left(log\right(sec\theta +tan\theta )}{d\left(sec\theta \right)}=\frac{\left(\frac{sec\theta tan\theta +{sec}^2\theta }{sec\theta +tan\theta }\right)}{sec\theta tan\theta }=\frac{1}{tan\theta }=cot\theta =cot\left(\frac{\pi }{4}\right)=1$