Write the interval in which `f(x)=sinx+cosx ,\ \ x in [0,\ pi//2]` is increasing.

Explanation

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

### Step 1: Find the derivative of the function
To find where the function is increasing, we first need to compute the derivative \( f'(x) \).

\[ f'(x) = \frac{d}{dx}(\sin x + \cos x) = \cos x - \sin x \]
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