The total derivative of a function does not give another function in the same way as the one-variable case.
12.
In economics, it is common for the total derivative to arise in the context of a system of equations.
13.
Now, we need the following relation about the total derivative of the density ( where we apply the chain rule ):
14.
This is another way of saying that the total derivative of price with respect to consumer income is greater than zero.
15.
Instead, the total derivative gives a function from the tangent bundle of the source to the tangent bundle of the target.
16.
Enhance " I ( E ) " by adding all the possible compositions of total derivatives applied to all its elements.
17.
Some authors prefer to use capital D to indicate the total derivative operator, as in " D " / " Dt ".
18.
Note that the integral on the left hand side is a function solely of time, and so the total derivative has been used.
19.
This is because the total derivative of a multivariable function has to record much more information than the derivative of a single-variable function.
20.
Applying an infinitesimal supersymmetry transformation to a chiral superfield results in yet another chiral superfield whose F-term, in particular, changes by a total derivative.
