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14.6 Directional Derivatives and the Gradient Vector We have done partial derivatives
 

Summary: 14.6 Directional Derivatives and the Gradient Vector
We have done partial derivatives
xf : rate of change of `f' in x-direction
yf : rate of change of `f' in y-direction
In this section, we will see the directional derivatives
rate of change of `f' in any given direction
1
Before defining the directional derivative, we study the
gradient of a function of two or more variables
Gradient of a function
Also called
gradient of `f'
For a function ( , , )f x y z , the gradient vector of ( , , )f x y z is
defined as
, ,x y zf f f f =
( , , ) ( , , ) ( , , ) ( , , )x yi j kf x y z f x y z f x y z f x y z = + +
Similar definition can be defined for functions of two or more variables.
f is a vector
2
Properties of f : (Same as derivatives)

  

Source: Ansari, Qamrul Hasan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals

 

Collections: Mathematics