Mathematical Analysis

Differential Calculus

What is a partial derivative?

Partial derivatives (seen written as the symbol δ) are derivatives of a function containing multiple variables that have all but the variable of interest held fixed during the differentiation. Thus, when a function f (x, y, …) depends on more than one variable, the partial derivative can be used to specify the derivative with respect to one or more variables. There are other terms, too: Partial derivatives that involve more than one variable are called mixed partial derivatives. And a differential equation expressing one or more quantities in terms of partial derivatives is called, logically, a partial differential equation. These equations are well known in physics and engineering, and most are notoriously difficult to solve.


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