Concept: Partial derivatives that do not have the same variable(s) held constant (at the same values?) are not the same derivative (editing)

Prerequisite concepts

Multivariable Calculus Derivatives can be found while holding one or more variables constant

Derivatives of multivariable functions can be found by holding one or more variables constant (subject to physical limitations).

The value of a partial derivative depends on the value(s) of what is held constant

FIXME: Is this really a statement about paths? I don't think we have path-related concepts.

Partial Derivative Machine Derivatives

Partial derivatives that do not have the same variable(s) held constant (at the same values?) are not the same derivative

FIXME

Representations used

NEEDS NAME

$\left(\frac{\partial f}{\partial x}\right)_y$

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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 You can flip a partial derivative if the same variable(s) are constant

Name the experiment I

Heat capacity lecture