Recently I encountered the Clausius-Clapeyron Equation, which was initially given to me in the form, $$\frac{dP}{dT}=\frac{\Delta H_{vap}}{RT^2}P$$ However I was then told that it could be rearranged to give, $$\frac{d \ln P}{dT}=\frac{\Delta H_{vap}}{RT^2}$$ and I wanted to know how this is done. If someone could show me how to rearrange it into this form it would be greatly appreciated.
I am aware this is a more of a chemistry equation but my question is about rearranging the equation and not the equation itself specifically so I thought that the maths SE would be more appropriate than Chem SE.
This is an application of the chain rule: $\frac{d}{dt}(\ln P)=\frac{1}{P}\cdot\frac{dP}{dt}$. Then combine this with the first equation and simplify.