# Differentiability at one point.

Definition 6.1.1   Let be a function defined on a neighborhood of . The function is differentiable at if the quotient has a finite limit for arbitrary close to . This limit is called the first derivative of at and is denoted by .

Example 6.1.2

Let and . Then we have:

Thus:

We proved that is differentiable at 1 and that .

Example 6.1.3

Let and . Then we have:

Thus

We proved that is differentiable at 2 and that .

Definition 6.1.4   Sometimes, we denote:

Noah Dana-Picard 2007-12-28