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# The Isothermal Bulk Modulus

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

### Highlights of the activity

- This small group activity is designed to give students practice with calculating partial derivatives via a change of variables.
- Students evaluate requested partial derivatives directly, or, if necessary, with a change of variables.
- The whole class discussion focuses on strategies that help to organize the solving process.

### Reasons to spend class time on the activity

We have found that students have difficulty keeping track of their work during changes of variables, particularly in cases when the given expressions are complex. In this small group activity, students practice evaluating partial derivatives, including one with an inaccessible variable. For the latter case, students must use a change of variables. At this point in the class, students may have two methods of changing variables under their belts: differential substitution and chain rule diagrams. Although both methods can reliably produce results, using chain rule diagrams helps prevent students from becoming “lost in the woods.”