## 6.2 Differentiability of Standard Functions

All of the standard functions are differentiable except at certain
singular points, as follows:

Polynomials are differentiable for all arguments.

A rational function
is differentiable except where q(x) = 0, where the function grows to infinity.
This happens in two ways, illustrated by .

Sines and cosines and exponents are differentiable everywhere but
tangents and secants are singular at certain values. (Where?)

The inverse functions to powers such as x^{1/2} and x^{1/3}
are differentiable where they are defined except where the functions they are
inverse to have 0 derivative.