The gradient is a vector operation in multivariable calculus that represents the direction and rate of maximum change of a scalar function at a given point in its domain. It is denoted by the symbol ∇ (called “nabla”) and acts on a scalar function f(x, y, z) to produce a vector-valued function.
The gradient of a scalar function f(x, y, z) is given by:
∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k
where i, j, and k are the standard unit vectors in the x, y, and z directions, respectively, and ∂f/∂x, ∂f/∂y, and ∂f/∂z are the partial derivatives of f with respect to x, y, and z.