Within $(0, 2\pi)$, on which interval is $f(x) = \sin x - \cos x$ strictly decreasing?

Explanation

1. 01

   $f'(x) = \cos x + \sin x = \sqrt{2}\sin\left(x + \frac{\pi}{4}\right)$.

2. 02

   This is negative when $x + \frac{\pi}{4}$ is between $\pi$ and $2\pi$, that is, $x$ between $\frac{3\pi}{4}$ and $\frac{7\pi}{4}$.