Table of Contents
What is Directional Derivative
Directional Derivative – Definition : The directional derivative of a function at a point P in a direction D is a measure of the rate of change of the function in that direction. It defined as the limit of the average rate of change of the function in the direction D as the length of the vector from P to D goes to zero.
Directional Derivative Definition
The directional derivative of a function is a derivative taken with respect to a particular vector direction. It measures the rate of change of the function in that direction.
The directional derivative of a function at a point is a derivative taken with respect to a particular vector direction. However it measures the rate of change of the function in that direction.
How to Find The Directional Derivative?
The directional derivative at a point (x, y) in a direction vector u is the derivative of the function f(x, y) in the direction u. However it denoted by Df(x, y) or DF(x, y) and given by
Df(x, y) = lim Δx→0 Δy→0
Df(x + Δx, y + Δy) – Df(x, y)
ΔxΔy
The directional derivative can computed using the following formula:
Df(x, y) = lim Δx→0 Δy→0
Df(x + Δx, y + Δy) – Df(x, y)
ΔxΔy
Directional derivative properties
The directional derivative of a scalar field at a point in a given direction is the derivative of the scalar field in that direction multiplied by the magnitude of the given direction.
More generally, the directional derivative of a vector field at a point in a given direction is the derivative of the vector field in that direction multiplied by the magnitude of the given direction.
The directional derivative is a particularly important tool in physics and engineering, where it used to calculate the rate of change of a quantity in a given direction.
Directional Derivative Formula
Function at point is a vector that points in direction of greatest rate of change of function at that point.
