Differentiate `x^(sin^(-1)x)` with respect to `sin^(-1)x` .

Explanation

To differentiate the function \( u = x^{\sin^{-1} x} \) with respect to \( v = \sin^{-1} x \), we will follow these steps:

### Step 1: Rewrite the function using logarithms
We start by taking the natural logarithm of both sides:
\[ \ln u = \ln(x^{\sin^{-1} x}) = \sin^{-1} x \cdot \ln x \]

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