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Total Derivative

  • Definition: The total derivative is the derivative with respect to t of the function y=f(t,u_1,...,u_m) that depends on the variable t not only directly but also via the intermediate variables u_1=u_1(t,u_1,...,u_m),...,u_m=u_m(t,u_1,...,u_m). It can be calculated using the formula (partial y)/(partial t)=[(partial f)/(partial t)]+[(partial f)/(partial u_1)][(partial u_1)/(partial t)]+...+[(partial f)/(partial u_m)][(partial u_m)/(partial t)].


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