If `f(x)=|cosx-sinx|` , find `f^(prime)(pi/6)` and `f^(prime)(pi/3)` .

Explanation

To find the derivatives \( f'(\frac{\pi}{6}) \) and \( f'(\frac{\pi}{3}) \) for the function \( f(x) = |\cos x - \sin x| \), we will first analyze the function and then differentiate it piecewise based on the intervals defined by the expression inside the modulus.

### Step 1: Analyze the function \( f(x) = |\cos x - \sin x| \)

The expression \( \cos x - \sin x \) can be positive or negative depending on the value of \( x \). We need to find the points where \( \cos x = \sin x \):

\[
\cos x = \sin x \implies \tan x = 1 \implies x = \frac{\pi}{4} + n\pi \quad (n \in \mathbb{Z})
...