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In Mathematics the gradient is a vector operator that, when applied to scalar function, makes a vector field that points in the direction of the greatest rate of change and has a magnitude equal to that rate.

The gradient is noted by:


where f is any scalar function.

Expanded, the gradient looks like this:

[∂f/∂x, ∂f/∂y, ∂f/∂z]

If f is only in terms of x and y (i.e. the equation is z =), just use the first two components.

Note: The gradient does not exist at points where the function is asmotic or undefined.