Prerequisite concepts
Variables can be held constant
When taking a derivative of a multivariable function, it is possible to consider a simpler situation in which some of the variables are considered to be constant.
Representations used
Derivatives can be found while holding one or more variables constant
There is a partial derivative in every direction at any point
Derivatives of multivariable functions can be found by holding one or more variables constant (subject to physical limitations).
Differentials are small changes or differences
Equations can be 'zapped with d' to relate differentials
Individual differentials can be manipulated algebraically
Total differentials are linear
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
The coefficients in a differentials equation are partial derivatives