NOTE 1 The gradient expresses the variation of the scalar field quantity from the given point to a point at an infinitesimal distance $\mathrm{d}s$ in the direction of a given unit vector e by the scalar product df = grad f ⋅ e ds.

NOTE 2 In orthonormal Cartesian coordinates, the three coordinates of the gradient are:

${\displaystyle \frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z}}$.

NOTE 3 The gradient of the scalar field f is denoted grad f or $\mathbf{\nabla }f$.