Prerequisite concepts
You can flip a partial derivative if the same variable(s) are constant
There might be experimental limits on which quantities you can measure
Differentials allow the finding of partial derivatives when a variable cannot be solved for
$\left(\frac{\partial f}{\partial x}\right)_y$
In other words,[\left(\frac{\partial y}{\partial z}\right)_z = \frac1{\left(\frac{\partial x}{\partial y}\right)_z}] Note that this equality is only true if the same variables are being held fixed on each side of the equality. This therefore relies on the thermodynamics notation that specifies what quantities are being held fixed for a partial derivative.
Instructor guide
eenametheexperiment2
Name the experiment: changing entropy
Representations used
$df$
$\left(\frac{\partial f}{\partial x}\right)_y$
Experiment