Confuing derivative

1. Jul 23, 2012

racnna

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

2. Jul 23, 2012

tiny-tim

3. Jul 23, 2012

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!

Last edited: Jul 23, 2012
4. Jul 23, 2012

tiny-tim

ooooh, it's T-time! :tongue2:

chain rule …

d(lnT)/dt = d(lnT)/T dT/dt

5. Jul 23, 2012

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...