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, then the directional derivative of a function ƒ is sometimes denoted as . In other notations
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—Rutherford Birchard Hayes (1822–1893)
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—Henry David Thoreau (1817–1862)