Editing Gradient (section)

===Cartesian coordinates===
In the three-dimensional [[Cartesian coordinate system]] with a [[Euclidean metric]], the gradient, if it exists, is given by

<math display="block">\nabla f = \frac{\partial f}{\partial x} \mathbf{i} + \frac{\partial f}{\partial y} \mathbf{j} + \frac{\partial f}{\partial z} \mathbf{k},</math>

where {{math|'''i'''}}, {{math|'''j'''}}, {{math|'''k'''}} are the [[standard basis|standard]] unit vectors in the directions of the {{math|''x''}}, {{math|''y''}} and {{math|''z''}} coordinates, respectively. For example, the gradient of the function
<math display="block">f(x,y,z)= 2x+3y^2-\sin(z)</math>
is
<math display="block">\nabla f(x, y, z) = 2\mathbf{i}+ 6y\mathbf{j} -\cos(z)\mathbf{k}.</math>
or 
<math display="block">\nabla f(x, y, z) = 
\begin{bmatrix}
 2 \\
 6y \\
 -\cos z
\end{bmatrix}.
</math>

In some applications it is customary to represent the gradient as a [[row vector]] or [[column vector]] of its components in a rectangular coordinate system; this article follows the convention of the gradient being a column vector, while the derivative is a row vector.