Gradient

In mathematics, the gradient is a generalization of the usual concept of derivative to functions of several variables. If f(x1, ..., xn) is a differentiable, real-valued function of several variables, its gradient is the vector whose components are the n partial derivatives of f. It is thus a vector-valued function. The Jacobian is the generalization of the gradient for vector-valued functions of several variables and differentiable maps between Euclidean spaces or, more generally, manifolds. A further generalization for a function between Banach spaces is the Fréchet derivative.

Gradient

In mathematics, the gradient is a generalization of the usual concept of derivative to functions of several variables. If f(x1, ..., xn) is a differentiable, real-valued function of several variables, its gradient is the vector whose components are the n partial derivatives of f. It is thus a vector-valued function. The Jacobian is the generalization of the gradient for vector-valued functions of several variables and differentiable maps between Euclidean spaces or, more generally, manifolds. A further generalization for a function between Banach spaces is the Fréchet derivative.