Editing Directional derivative (section)

== Normal derivative ==

A '''normal derivative''' is a directional derivative taken in the direction normal (that is, [[orthogonal]]) to some surface in space, or more generally along a [[normal vector]] field orthogonal to some [[hypersurface]]. See for example [[Neumann boundary condition]]. If the normal direction is denoted by <math>\mathbf{n}</math>, then the normal derivative of a function ''f'' is sometimes denoted as <math display="inline">\frac{ \partial f}{\partial \mathbf{n}}</math>. In other notations,
<math display="block">\frac{ \partial f}{\partial \mathbf{n}} = \nabla f(\mathbf{x}) \cdot \mathbf{n} = \nabla_{\mathbf{n}}{f}(\mathbf{x}) = \frac{\partial f}{\partial \mathbf{x}} \cdot \mathbf{n} = Df(\mathbf{x})[\mathbf{n}].</math>