directional derivative
Let be an open set in and is a differentiable function. If and , then the directional derivative of in the direction of is
In other words, measures how changes in the direction of from .
Properties
Let .
-
1.
is linear in . If and , then
In particular, .
- 2.
Example
For example, if , and we wanted to find the derivative at the point in the direction , our equation would be
Title | directional derivative |
Canonical name | DirectionalDerivative |
Date of creation | 2013-03-22 11:58:37 |
Last modified on | 2013-03-22 11:58:37 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 15 |
Author | matte (1858) |
Entry type | Definition |
Classification | msc 26B12 |
Classification | msc 26B10 |
Synonym | derivative with respect to a vector |
Synonym | partial derivative with respect to a vector |
Related topic | PartialDerivative |
Related topic | Derivative |
Related topic | DerivativeNotation |
Related topic | JacobianMatrix |
Related topic | Gradient |
Related topic | FixedPointsOfNormalFunctions |
Related topic | HessianMatrix |