Total derivative

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In mathematics, a total derivative of a function of several variables is its derivative with respect to one of those variables, but taking into account eventual indirect dependencies, i.e. the fact that the other variables may depend on this variable. This is in contrast with the partial derivative at which other variables are thought constant.

For example, the total derivative of the function f(x,y,z) with respect to the variable x is

\frac{\mathrm df}{\mathrm dx}=\frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} \frac{\partial y}{\partial x} + \frac{\partial f}{\partial z} \frac{\partial z}{\partial x}.


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