In the mathematical field of differential calculus, a total derivative or full derivative of a function of several variables, e.g., , , , etc., with respect to an exogenous argument, e.g., , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as its indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative(). Calculation of the total derivative of with respect to does not assume that the other arguments are constant while varies; instead, it allows the other arguments to depend on . The total derivative adds in these indirect dependencies to find the overall dependency of on For example, the total derivative of with respect to is which simplifies to Consider multiplying both sides of the equation by the differential : The result is the differential change in, or total differential of, the function . Because depends on , some of that change will be due to the partial derivative of with respect to . However, some of that change will also be due to the partial derivatives of with respect to the variables and . So, the differential is applied to the total derivatives of and to find differentials and , which can then be used to find the contribution to . "Total derivative" is sometimes also used as a synonym for the material derivative, in fluid mechanics.

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