Question-28 The value of \frac{d}{d x}\left[\tan ^{-1}\left(\frac{a+x}{1-a x}\right)\right] is, where a is constant a, x \in R^{+}, a x<1
A)
\frac{1}{1+x^{2}}B)
-\frac{1}{1+x^{2}}C)
\frac{a}{1+x^{2}}D)
\frac{-a}{1+x^{2}}Answer: A)
Explanation
\begin{aligned} & \frac{d}{d x}\left[\tan ^{-1}\left(\frac{a+x}{1-a x}\right)\right]=\frac{d}{d x}\left[\tan ^{-1} a+\tan ^{-1} x\right] \ & =\frac{1}{1+x^{2}} \end{aligned}