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Gradient of a Function

There is an easier way to find the directional derivatives of f(x, y) using the partial derivatives. It is convenient to combine the partial derivatives into a vector called the gradient of f.


The gradient of a function z = f(x, y), denoted by grad z or grad f, is defined by


In functional notation,

grad f = fx(a,b)i + fy(a,b)j.

Thus grad f is the vector valued function of two variables whose x and y components are the partial derivatives fx and fy (Figure 13.1.3). Sometimes the notation ∇f or ∇z is used for the gradient.


Figure 13.1.3

Last Update: 2006-11-05