Prerequisite concepts
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
While it is relatively easy to imagine very, very small changes in physical values, there are often experimental limits on how small of a change can be measured. When designing and conducting experiments, there is a tension between these experimental limitations and normative representations of functions as smooth lines or
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
Instructor guide
eeice
Ice calorimetry lab
Representations used
Experiment
$\left(\frac{\partial f}{\partial x}\right)_y$