An **exterior derivative** is an extension of a derivative to higher-dimensional differential forms on differentiable manifolds. It allows for derivatives to be expressed in coordinate-free form, and is the basis for the generalized Stokes' theorem. In general, the exterior derivative of an *n*-form is an *n+1* form.

## Specific examples of exterior derivatives

- Gradient (0-form to 1-form)
- Curl (1-form to 2-form)
- Divergence (2-form to 3-form)