`tan^(-1)((7x)/(1-12x^(2)))`

Explanation

To solve the problem of differentiating \( y = \tan^{-1}\left(\frac{7x}{1 - 12x^2}\right) \), we will follow these steps:

### Step 1: Recognize the Identity
We can use the identity for the tangent inverse function:
\[ \tan^{-1}\left(\frac{a + b}{1 - ab}\right) = \tan^{-1}(a) + \tan^{-1}(b) \]
In our case, we can express \( \frac{7x}{1 - 12x^2} \) in the form of this identity by letting \( a = 4x \) and \( b = 3x \).
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