Consider the following statements:
Assertion $(A)$: For $x \in \mathbb{R}-\{1\}$, $\frac{d}{dx}\left(\tan^{-1}\left(\frac{1+x}{1-x}\right)\right) = \frac{d}{dx}\left(\tan^{-1} x\right)$.
Reason $(R)$: For $x < 1$, $\tan^{-1}\left(\frac{1+x}{1-x}\right) = \frac{\pi}{4} + \tan^{-1} x$, and for $x > 1$, $\tan^{-1}\left(\frac{1+x}{1-x}\right) = -\frac{3\pi}{4} + \tan^{-1} x$.
The correct answer is:

• A
  Both $(A)$ and $(R)$ are true, $(R)$ is the correct explanation of $(A)$
• B
  Both $(A)$ and $(R)$ are true, $(R)$ is not the correct explanation of $(A)$
• C
  $(A)$ is true, but $(R)$ is false
• D
  $(A)$ is false, but $(R)$ is true