partial derivative


partial derivative

noun

Definition of PARTIAL DERIVATIVE

:  the derivative of a function of several variables with respect to one of them and with the remaining variables treated as constants

First Known Use of PARTIAL DERIVATIVE

1889

partial derivative

noun    (Concise Encyclopedia)

In differential calculus, the derivative of a function of several variables with respect to change in just one of its variables. Partial derivatives are useful in analyzing surfaces for maximum and minimum points and give rise to partial differential equations. As with ordinary derivatives, a first partial derivative represents a rate of change or a slope of a tangent line. For a three-dimensional surface, two first partial derivatives represent the slope in each of two perpendicular directions. Second, third, and higher partial derivatives give more information about how the function changes at any point.

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