Unclear differential equation from a thermodynamics textbook

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.
  • #1
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Homework Statement
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Relevant Equations
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In the thermodynamics textbook there is written: 𝛿𝐴 = 𝑇𝑑𝑆 βˆ’ π‘‘π‘ˆ = 𝑑(𝑇𝑆) βˆ’ 𝑆𝑑𝑇 βˆ’ π‘‘π‘ˆ = βˆ’π‘‘(π‘ˆ βˆ’ 𝑇𝑆) βˆ’ 𝑆𝑑𝑇 = βˆ’π‘‘πΉ βˆ’ 𝑆𝑑𝑇
How did we get the bolded area from TdS? Is that property of derivative, integral, or something else :/
 
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  • #2
Product rule
 
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  • #3
Sorry for being so terse. I was posting from my phone.

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