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The slope of a line, at a particular point. A horizontal line has gradient 0; a vertical line has infinite (undefined) gradient.
The gradient of a straight line is equal to the change in y coordinate divided by the corresponding change in x coordinate.
Gradient is the tangent of the angle between the line and the horizontal.

Given f : R^m → R differentiable at a ∈ R^m , the gradient of f at a is

∇f = m ∑ j=1  ej f′ [ a ] ( ej ) ,

read `grad f,' where { e_j }_j=1^m is the standard basis for R^m .
The gradient of f is a vector whose j th component is the j th partial derivative of f , and for any vector h , we have f^′ [ a ](h) = h ·∇f .

In 3 dimensions the gradient of a scalar function f(x,y,z) is the vector:

∇f =          ∂f ∂x ∂f ∂y ∂f ∂z         