Concept

Directional derivative

Summary
A directional derivative is a concept in multivariable calculus that measures the rate at which a function changes in a particular direction at a given point. The directional derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. The directional derivative of a scalar function f with respect to a vector v at a point (e.g., position) x may be denoted by any of the following: \nabla_{\mathbf{v}}{f}(\mathbf{x})=f'\mathbf{v}(\mathbf{x})=D\mathbf{v}f(\mathbf{x})=Df(\mathbf{x})(\mathbf{v})=\partial_\mathbf{v}f(\mathbf{x})=\mathbf{v}\cdot{\nabla f(\mathbf{x})}=\mathbf{v}\cdot \frac{\partial f(\mathbf{x})}{\partial\mathbf{x}}. It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the curvilinear coordinate curves, all other coordin
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading