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Concept# Partial derivative

Summary

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others 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 partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by
It can be thought of as the rate of change of the function in the x-direction.
Sometimes, for z=f(x, y, \ldots), the partial derivative of z with respect to x is denoted as \tfrac{\partial z}{\partial x}. Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in:
f'_x(x, y, \ldots), \frac{\partial f}{\partial x}

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