In my AI textbook there is this paragraph, without any explanation.

The sigmoid function is defined as follows

$$\sigma (x) = \frac{1}{1+e^{-x}}.$$

This function is easy to differentiate because

$$\frac{d\sigma (x)}{d(x)} = \sigma (x)\cdot (1-\sigma(x)).$$

It has been a long time since I've taken differential equations, so could anyone tell me how they got from the first equation to the second?