If `y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2])` and `0 < x < 1,` then find `(dy)/(dx)`

Explanation

To solve the problem, we need to differentiate the given function:

Given:
\[ y = \sin^{-1}\left[x\sqrt{1-x} - \sqrt{x}\sqrt{1-x^2}\right] \]

### Step 1: Simplify the expression inside the inverse sine function
Let:
\[ z = x\sqrt{1-x} - \sqrt{x}\sqrt{1-x^2} \]
...