A gradient represents the slope in a space. Earlier,
we used partial differentiation with respect to 'x' to see how the slope
changes along the x-axis on a three-dimensional graph while keeping 'y'
constant. A gradient, however, involves finding the partial derivatives for all
variables and representing them in matrix form.
Gradient (Cited from
www.syncfusion.com)
Consider the function f(x, y) = 2x2 + 2y2,
which represents a three-dimensional plane. To find the rate of change on the
surface, each variable is partially differentiated, yielding 4x and 4y,
respectively. These partial derivatives can then be combined into matrix form.
If at point (x, y) = (-2, -2), the gradient is (-8,
-8), meaning both 'x' and 'y' are decreasing with a magnitude of 8. At point
(x, y) = (1, 1), the gradient is (4, 4), meaning both 'x' and 'y' are
increasing with a magnitude of 4.
The symbol for gradient, ∇, is called the nabla or del operator.
