Definition:Partial Derivative/Notation

Notation for Partial Derivative
There are various notations for the $i$th partial derivative of a function:


 * $\dfrac {\partial f} {\partial x_i}$
 * $\dfrac {\partial} {\partial x_i} f$
 * $f_{x_i} \left({\mathbf x}\right)$
 * $f_{x_i} \left({x_1, x_2, \cdots, x_n}\right)$
 * $f_{x_i}$
 * $\partial_{x_i}f$
 * $\partial_i f$
 * $D_i f$


 * $\dfrac {\partial z} {\partial x_i}$
 * $z_{x_i}$

where $z = f \left({x_1, x_2, \cdots, x_n}\right)$.