Prerequisite concepts
Individual differentials can be manipulated algebraically
FIXME: What? One can do algebra with differentials and reinterpret them as partial derivatives. Can treat like a variable
Differentials allow the finding of partial derivatives when a variable cannot be solved for
There might be experimental limits on which quantities you can measure
You can flip a partial derivative if the same variable(s) are constant
Because total differentials are linear, one can find the total differential and then solve algebraically to obtain partial derivatives that might not be obtainable though differentiation.