I've never *why* that is, that if you have something like this:

$$\frac{d}{dx}[x^2-3x]$$

It can be written (and must in order to solve as far as I'm concerned) as:

$$\frac{d}{dx}[x^2-3x] = \frac{d}{dx}[x^2]\ - \frac{d}{dx}[3x]$$

Could someone explain the intuition behind this?