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# Deriving Change of Variables

**Keywords:**Interlude, Partial Derivative, Total Differential, Small Group Activity, PDM, Change of Variables, Differentials

### Highlights of the activity

- This small group activity is designed to provide students with practice in using a change of variables procedure for partial derivatives and total differentials.
- Students use the variables from the Partial Derivative Machine (PDM) to practice the mathematical technique of change of variables when given a partial derivative that cannot be explicitly measured.
- The whole class discussion focuses on how students manipulated the mathematical quantities to arrive at a total differential from which they could successfully extract the requested derivative.

### Reasons to spend class time on the activity

This activity occurs during the “Interlude”, a brief course on the basic mathematics used in the “Energy and Entropy” Paradigm. This course primarily focuses on an introduction to partial derivatives and total differentials. We would like our students to have an understanding of how to measure partial derivatives, as well as understand that the “thing held constant” has both physical and mathematical consequences. This activity uses the variables associated with the Partial Derivative Machine (PDM) to introduce students to the change of variables procedure for partial derivatives and total differentials, using familiar and physically significant variables.