Total derivative of poison

Question

I’m studying Adiabatic pressure change by reading text book and encounter this equation

$(1)\:\:\:\:\:\:PV^γ=constant $

Total Derivative of $(1)$ will be $∂P/P=-γ∂V/V $ Can somebody explain process of this equation?

Answer 1

Just take the differential $$ V^{\gamma}dP+P\gamma V^{\gamma-1}dV=0 $$ and divide by $PV^{\gamma}$.

Answer 2

$PV^\gamma=c \\ \Rightarrow P = cV^{-\gamma} \\ \displaystyle \Rightarrow \frac {dP}{dV} = -\gamma c V^{-\gamma-1} \\ \displaystyle \Rightarrow \frac {dP}{dV} = - \gamma \frac P V$