Differentiate `tan^(-1)((1+2x)/(1-2x))` with respect to `sqrt(1+4x^2)` .

Explanation

To differentiate \( \tan^{-1}\left(\frac{1 + 2x}{1 - 2x}\right) \) with respect to \( \sqrt{1 + 4x^2} \), we will follow these steps:

### Step 1: Define the Functions
Let:
- \( u = \tan^{-1}\left(\frac{1 + 2x}{1 - 2x}\right) \)
- \( v = \sqrt{1 + 4x^2} \)

We need to find \( \frac{du}{dv} \).
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