Editing Gradient (section)

===Cylindrical and spherical coordinates===
{{main|Del in cylindrical and spherical coordinates}}

In [[cylindrical coordinate system#Definition|cylindrical coordinates]], the gradient is given by:<ref name="Schey-1992" />

<math display="block">\nabla f(\rho, \varphi, z) = \frac{\partial f}{\partial \rho}\mathbf{e}_\rho + \frac{1}{\rho}\frac{\partial f}{\partial \varphi}\mathbf{e}_\varphi + \frac{\partial f}{\partial z}\mathbf{e}_z,</math>

where {{math|''ρ''}} is the axial distance, {{math|''φ''}} is the azimuthal or azimuth angle, {{math|''z''}} is the axial coordinate, and {{math|'''e'''<sub>''ρ''</sub>}}, {{math|'''e'''<sub>''φ''</sub>}} and {{math|'''e'''<sub>''z''</sub>}} are unit vectors pointing along the coordinate directions.

In [[spherical coordinate system#Definition|spherical coordinates]] with a Euclidean metric, the gradient is given by:<ref name="Schey-1992">{{harvnb|Schey|1992|pp=139–142}}.</ref>

<math display="block">\nabla f(r, \theta, \varphi) = \frac{\partial f}{\partial r}\mathbf{e}_r + \frac{1}{r}\frac{\partial f}{\partial \theta}\mathbf{e}_\theta + \frac{1}{r \sin\theta}\frac{\partial f}{\partial \varphi}\mathbf{e}_\varphi,</math>

where {{math|''r''}} is the radial distance, {{math|''φ''}} is the azimuthal angle and {{math|''θ''}} is the polar angle, and {{math|'''e'''<sub>''r''</sub>}}, {{math|'''e'''<sub>''θ''</sub>}} and {{math|'''e'''<sub>''φ''</sub>}} are again local unit vectors pointing in the coordinate directions (that is, the normalized [[Curvilinear coordinates#Covariant and contravariant bases|covariant basis]]).

For the gradient in other [[orthogonal coordinate system]]s, see [[Orthogonal coordinates#Differential operators in three dimensions|Orthogonal coordinates (Differential operators in three dimensions)]].