Differentiate the following functions with respect to `x :` `tan^(-1)((a+x)/(1-a x))`

Explanation

To differentiate the function \( y = \tan^{-1}\left(\frac{a+x}{1-ax}\right) \) with respect to \( x \), we can follow these steps:

### Step 1: Recognize the Inverse Trigonometric Identity
We can use the identity for the tangent inverse function:
\[ \tan^{-1}(u) + \tan^{-1}(v) = \tan^{-1}\left(\frac{u+v}{1-uv}\right) \]
In our case, we can express \( y \) as:
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