In mathematics, the gradient is a term used for the differential operator, which is applied to a scalar-valued differentiable function of several variables to generate a vector field. The gradient of a function is represented by the symbol ∇f or ∇→f, where ∇ denotes the vector differential operator, del. The gradient of a function is defined as the unique vector field whose dot product with any vector v at each point x is the directional derivative of f along v. The gradient plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. The gradient is also useful to measure how a scalar field changes in other directions, rather than just the direction of greatest change, by taking a dot product. The gradient is often referred to as the slope of a line.