In this section we will introduce a function called "Lambert's W", which is written: W(t). W(t) has properties analogous to the natural log function ln(t), and so we will first review some of its properties.

The Natural Log Function: ln(t)

Recall that the function ln(t) is the "composition inverse" of the exponential function, i.e. it is the unique function with the following properties.

Lambert's W Function: W(t)

Next, we have another pair of functions like ln(t) and exp(t), W(t) and ewp(t), that are composition inverses of each other.

Here is a plot of all four of the above functions:

The Chain Rule and the Derivative of W(t): W'(t)