In mathematics, a differential operator applied to a three-dimensional vector-valued function to yield a vector whose three components are the
The symbol for gradient is ∇. Thus, the gradient of a function f , written grad f , or ∇ f , is ∇ f = i f x + j f y + k f z where f x , f y , and f z are the first partial derivatives of f and the vectors i , j , and k are the unit vectors of the {{link=vector space">vector space . If in physics, for example, f is a temperature field (giving the temperature at every point in a space), ∇ f is the direction of the heat-flow vector in the field.