Why Does the Chain Rule in Thermodynamics Include a Negative Sign?

korialstasz
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I'm trying to understand why

$$\left(\frac{\partial P}{\partial T}\right)_V = -\left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial V}{\partial T}\right)_P$$

where does the minus sign come from?
 
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What is dV(P,T) in terms of dP and dT?
 

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