# Unclear differential equation from a thermodynamics textbook

• NODARman
In summary, a differential equation is an equation that relates a variable's rate of change to the variables themselves, commonly used to describe the behavior of a system over time. It can be unclear if it lacks important information, has multiple solutions, or uses confusing notation. Understanding differential equations is crucial in thermodynamics for predicting and analyzing energy, temperature, and other variables in a system. Techniques for solving unclear differential equations include separation of variables, substitution, and using specific conditions. To improve understanding, one can practice solving equations, study thermodynamics principles, and seek help from a tutor or professor.

#### NODARman

Homework Statement
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Relevant Equations
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In the thermodynamics textbook there is written: πΏπ΄ = πππ β ππ = π(ππ) β πππ β ππ = βπ(π β ππ) β πππ = βππΉ β πππ
How did we get the bolded area from TdS? Is that property of derivative, integral, or something else :/

Product rule

topsquark and NODARman
Sorry for being so terse. I was posting from my phone.

Apply the product rule to ##TS##. ##d(TS) = ?##.

topsquark