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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.
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