Differentiate the following w.r.t. x:
`(sinx)^x+sin^(-1)sqrt(x)`

Explanation

To differentiate the function \( y = (\sin x)^x + \sin^{-1}(\sqrt{x}) \) with respect to \( x \), we will break it down into two parts: \( u = (\sin x)^x \) and \( v = \sin^{-1}(\sqrt{x}) \). We will find the derivatives \( \frac{du}{dx} \) and \( \frac{dv}{dx} \) separately and then combine them.

### Step 1: Differentiate \( u = (\sin x)^x \)

To differentiate \( u \), we will use logarithmic differentiation.

1. Take the natural logarithm of both sides:
\[
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