Higher Order Partial Derivatives

Second and higher order partial derivatives are defined analogously to the higher order derivatives of univariate functions.
In mathematics, partial derivative of a function of several variables is its derivative with respect to one of those variables while the other variables are held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.
The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differences.

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