Derivative of Pressure/Temperature: Explained

[racnna]

can someone please explain this?

$$\frac{d}{dt} \frac{P}{T}=\frac{1}{T} ( \frac{dP}{dt}- \frac{dlnT}{dt})$$

 

[tiny-tim]

(there's a P missing on the RHS )

product rule and chain rule …

what is d(lnT)/dt ? ​

 

[racnna]

im not sure...

but i just tried quotient rule and it worked out?...
$$\frac{d}{dt} \frac{P}{T}= \frac{T \frac{dP}{dt}-P \frac{dT}{dt}}{T^2}=\frac{1}{T} \frac{dP}{dt} - \frac{P}{T^2} \frac{dT}{dt}$$ ...etc.
how exactly do you implement chain rule after you use product rule? i would like to know. thanks in advance!

 

[tiny-tim]

ooooh, it's T-time!

chain rule …

d(lnT)/dt = d(lnT)/T dT/dt ​

 

[racnna]

thanks!...i need to get used to using the chain rule...we never really used it much in my calculus classes from back in the day...