The first derivative of the function `[cos^(-1)(sin sqrt((1+x)/2))+x^x]` with respect to `x` at `x = 1` is

Options

A. `3//4`
B. 0
C. `1//2`
D. `-1//2`

Explanation

To find the first derivative of the function \( y = \cos^{-1}(\sin(\sqrt{\frac{1+x}{2}})) + x^x \) with respect to \( x \) at \( x = 1 \), we will follow these steps:

### Step 1: Rewrite the Function
We start with the function:
\[ y = \cos^{-1}(\sin(\sqrt{\frac{1+x}{2}})) + x^x \]

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