Prerequisite concepts
Equations can be 'zapped with d' to relate differentials
Individual differentials can be manipulated algebraically
Total differentials are linear
Differentials are small changes or differences
FIXME: Does the difference between zapping with d and taking the total differential need to be articulated?
FIXME: What? One can do algebra with differentials and reinterpret them as partial derivatives. Can treat like a variable
No matter how complicated a multivariable function is when written as an equation, the total differential of that function will be linear in the differential terms. In other words: $dF(x,y,z)=A dx + B dy + C dz.$
The coefficients in a differentials equation are partial derivatives
There are experimental limits to how $small$ of a change can be measured
The derivative can be interpreted physically
Partial derivatives that do not have the same variable(s) held constant (at the same values?) are not the same derivative
FIXME
Differentials allow the finding of partial derivatives when a variable cannot be solved for
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.