Search any question & find its solution
Question:
Answered & Verified by Expert
If $y=\tan ^{-1}(\sec x+\tan x), \frac{-\pi}{2} < x < \frac{\pi}{2}$, then find $\frac{d y}{d x}$.
Solution:
1776 Upvotes
Verified Answer
$$
\text \begin{aligned}
\therefore & \frac{d y}{d x}=\frac{d}{d x} \tan ^{-1}(\sec x+\tan x) \\
=& \frac{1}{1+(\sec x+\tan x)^2} \cdot \frac{d}{d x}(\sec x+\tan x) \\
=& {\left[\because \frac{d}{d x}\left(\tan ^{-1} x\right)=\frac{1}{1+x^2}\right] } \\
=& \frac{1}{2}
\end{aligned}
$$
\text \begin{aligned}
\therefore & \frac{d y}{d x}=\frac{d}{d x} \tan ^{-1}(\sec x+\tan x) \\
=& \frac{1}{1+(\sec x+\tan x)^2} \cdot \frac{d}{d x}(\sec x+\tan x) \\
=& {\left[\because \frac{d}{d x}\left(\tan ^{-1} x\right)=\frac{1}{1+x^2}\right] } \\
=& \frac{1}{2}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.