Gradient
![In the above two images, the values of the function are represented in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows.](/Images/godic/202501/16/Gradient2.svg1026.png")
![Gradient of the 2-d function f(x, y) = xe−(x2 + y2) is plotted as blue arrows over the pseudocolor plot of the function.](/Images/godic/202501/16/lossy-page1-350px-Gradient_of_a_Function.tif1026.jpg")
![The gradient of the function f(x,y) = −(cos2x + cos2y)2 depicted as a projected vector field on the bottom plane.](/Images/godic/202501/16/Gradient_Visual.svg1026.png")
In mathematics, the gradient is a generalization of the usual concept of derivative of a function in one dimension to a function in several dimensions. If f(x1, ..., xn) is a differentiable, scalar-valued function of standard Cartesian coordinates in Euclidean space, its gradient is the vector whose components are the n partial derivatives of f. It is thus a vector-valued function.