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# Derivatives and Chain Rules

## Prerequisites

Students should be able to:

• Recognize the traditional calculus notation for partial derivatives (i.e., $\partial f/\partial x$).
• Calculate a partial derivative given a symbolic expression and the variable(s) to be held constant.
• Determine a total differential by zapping with d.
• Write the thermodynamic identity for both the Partial Derivative Machine and for a gas in a piston.
• Reason about the physical quantities related to the Partial Derivative Machine.

## In-class Content

• ??? (Lecture: 20 min)
• New Surfaces activity - “Squishability” of Water Vapor (SGA - 20 min)

## Homework for Energy and Entropy

1. (mbTreeDiagramMath) Use Tree Diagrams to find chain rules.

2. (mbCyclic) Check cyclic chain rule for realistic equation of state

3. (mbParamagnet) Use chain rules to solve physics problem

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