# Higher degree derivatives.

Definition 6.10.1   Let be a function, differentiable on an neighborhood of . If is differentiable at , its first derivative is called the the second derivative of at . By induction we define the derivative of a function at a point ; we denote it by .

Example 6.10.2   Take . Then, for every , we have:

Example 6.10.3
1. If , then for every , we have:

2. If , then for every .
3. If , then we have:

(Check this by induction!)

Example 6.10.4   Let be the function defined by

Subsections
Noah Dana-Picard 2007-12-28