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A total derivative of a multivariable function of several variables, each of which is a function of another argument, is the derivative of the function with respect to said argument. it is equal to the sum of the partial derivatives with respect to each variable times the derivative of that variable with respect to the independent variable. For example, given a function , and with being functions of , The formula for a total derivative is a direct result of the chain rule.

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  • Total derivative
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  • A total derivative of a multivariable function of several variables, each of which is a function of another argument, is the derivative of the function with respect to said argument. it is equal to the sum of the partial derivatives with respect to each variable times the derivative of that variable with respect to the independent variable. For example, given a function , and with being functions of , The formula for a total derivative is a direct result of the chain rule.
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  • A total derivative of a multivariable function of several variables, each of which is a function of another argument, is the derivative of the function with respect to said argument. it is equal to the sum of the partial derivatives with respect to each variable times the derivative of that variable with respect to the independent variable. For example, given a function , and with being functions of , The formula for a total derivative is a direct result of the chain rule. Total derivatives are often used in related rates problems; for example, finding the rate of change of volume when two parameters are changing with time.
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