Prerequisite concepts
There might be experimental limits on which quantities you can measure
Differentials are small chunks
While it may be possible to conceptualize a particular derivative, such as $\left(\frac{\partial U}{\partial S}\right)_{V},$ Where $U$ is internal energy, $S$ is entropy, and $V$ is volume, that does not mean that the particular derivative can be directly measured. In the above example, the entropy $S$ is not measurable.
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
There are experimental limits to how $small$ of a change can be measured
The coefficients in a differentials equation are partial derivatives
While the constituents of a derivative (the $f$ and $x$ in $\frac{df}{dx}$) can have physical interpretations, the derivative itself can have a different physical interpretation. For example, $\frac{dx}{dt}$ is a velocity. FIXME: find a better example
FIXME
Instructor guide
eenametheexperiment
Name the experiment I
FIXME this is a cool lab.
Representations used
Experiment
$\left(\frac{\partial f}{\partial x}\right)_y$