If `f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2)` is `(sqrt(pi))/6` (b) `-sqrt(pi//6)` `1//sqrt(6)` (d) `pi//sqrt(6)`

Options

A. `sqrt(pi//6)`
B. `-sqrt(pi//6)`
C. `1//sqrt(6)`
D. `pi//sqrt(6)`

Explanation

To find \( f'(\frac{\sqrt{\pi}}{2}) \) for the function \( f(x) = \sqrt{1 + \cos^2(x^2)} \), we will follow these steps:

### Step 1: Define the function
We have:
\[ f(x) = \sqrt{1 + \cos^2(x^2)} \]

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