Directional Derivative Formula
Calculating the directional derivative involves the dot product of the gradient and the direction vector. In simple terms, for a function f, the directional derivative Dv(f) is given by:
Dv(f) = ∇f · v
where:
- ∇f represents Gradient of Function
- v is Direction Vector Along which we Want to Find Derivative
Directional Derivative
Directional Derivative measures how a function changes along a specified direction at a given point, providing insights into its rate of change in that direction. Directional Derivative can be defined as:
Dv(f) = ∇f · v
In this article, we will learn about the directional derivative, its meaning, definition, steps to calculate the directional derivative, directional derivative in three dimensions, and others in detail.
Table of Content
- What is a Directional Derivative?
- Directional Derivative Definition
- Directional Derivative Formula
- How to Calculate Directional Derivative
- Directional Derivative Formula in Vector Calculus
- Directional Derivative in Different Coordinate Systems
- Directional Derivative in Cartesian Coordinates
- Directional Derivative in Cylindrical Coordinates
- Directional Derivative in Spherical Coordinates
- Properties of Directional Derivative
- Linearity and Directional Derivative
- Directional Derivative Gradient
- Difference Between Directional Derivative and Partial Derivative
- Directional Derivative Examples
- Practice Problems on Directional Derivative