## 8.1 Derivatives of the Basic Functions

Since we define standard functions to be obtainable by applying a fixed set
of operations (arithmetic ones, substitution and inversion) to combinations
of three original functions, we can differentiate any standard function if we
know how to differentiate each of the three functions, and how to differentiate
a function obtained from others by each of the operations in terms of the derivatives
of the others.

The derivatives of the three basic functions are as follows

With rules for handling each operation, the task of differentiation of a standard
function requires only parsing its definition to break it down into individual
operations, and then applying the appropriate rule for each.

To do so we need rules for the following.