Differentiate w.r.t. x the function `sin^(-1)(xsqrt(x)),0lt=xlt=1`

Explanation

To differentiate the function \( f(x) = \sin^{-1}(x\sqrt{x}) \) with respect to \( x \), we will follow the steps outlined below:

### Step 1: Identify the function and its composition
The function we need to differentiate is:
\[ f(x) = \sin^{-1}(x\sqrt{x}) \]
Here, \( g(x) = x\sqrt{x} = x^{3/2} \) is the inner function.
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