Differentiate `sin^(-1)x` w.r.t. `tan^(-1)x`.

Explanation

To differentiate \( \sin^{-1} x \) with respect to \( \tan^{-1} x \), we can use the chain rule. Let's denote:

- \( u = \sin^{-1} x \)
- \( v = \tan^{-1} x \)

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

### Step 1: Find \( \frac{du}{dx} \)
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