Definition:Partial Derivative/Notation

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