Separate the interval `[0,\ pi//2]` into sub-intervals in which `f(x)=sin^4x+cos^4x` is increasing or decreasing.

Explanation

To determine where the function \( f(x) = \sin^4 x + \cos^4 x \) is increasing or decreasing on the interval \( [0, \frac{\pi}{2}] \), we will follow these steps:

### Step 1: Find the derivative of the function
We start by finding the derivative \( f'(x) \) of the function \( f(x) \).

\[ f(x) = \sin^4 x + \cos^4 x \]
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