Definition:Partial Derivative/Notation

Notation for Partial Derivative

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

• $\dfrac {\partial f} {\partial x_i}$
• $\dfrac {\partial} {\partial x_i} f$
• $\map {f_{x_i} } {\mathbf x}$
• $\map {f_{x_i} } {x_1, x_2, \cdots, x_n}$
• $f_{x_i}$
• $\partial_{x_i}f$
• $\partial_i f$
• $D_i f$

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

where $z = \map f {x_1, x_2, \cdots, x_n}$.

Sources

• 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (previous) ... (next): $1$ Partial Differentiation: $\S 1$. Introduction: $1.1$ Partial Derivatives