Show that the function `f(x)=cot^(-1)(sinx+cosx)` is decreasing on `(0,\ pi//4)` and increasing on `(pi//4,\ pi//2)` .

Explanation

To show that the function \( f(x) = \cot^{-1}(\sin x + \cos x) \) is decreasing on \( (0, \frac{\pi}{4}) \) and increasing on \( (\frac{\pi}{4}, \frac{\pi}{2}) \), we will find the derivative \( f'(x) \) and analyze its sign in the specified intervals.

### Step 1: Find the derivative \( f'(x) \)

The derivative of \( \cot^{-1}(u) \) where \( u = \sin x + \cos x \) is given by:

\[
f'(x) = -\frac{1}{1 + u^2} \cdot \frac{du}{dx}
...