Total Derivative
There are at least two meanings of the term "total derivative" in mathematics.
The first is as an alternate term for the convective derivative.
The second meaning of 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
The total derivative of a function f(t,x,y,...) with respect to t is implemented in the Wolfram Language as Dt [f[t, x, y, ...], t].
See also
Convective Derivative, Exact Differential, Exterior DerivativeExplore with Wolfram|Alpha
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References
Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia." Dordrecht, Netherlands: Reidel, p. 228, 1988.Referenced on Wolfram|Alpha
Total DerivativeCite this as:
Weisstein, Eric W. "Total Derivative." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TotalDerivative.html