Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
theEric
Group Title
Hi! I'm looking at an example from my book and I'm hoping somebody can explain this. It's in the first chapter, but I don't want to skip out on anything. Thanks! Here is the issue:
My book says that \(\dfrac{dp/dt}{p900}=\dfrac{1}{2}\) where \(p\neq 900\). Theennn... "By the chain rule the left side of [that equation] is the derivative of \(\ln\leftp900\right\) with respect to \(t\), so we have
\(\dfrac{d}{dt} \ln\left p900\right=\dfrac{1}{2}\)"
My issue is that I'm missing something. I see that \(\cancel{\dfrac{d}{dt}\dfrac{1}{p900}= \ln \left p900\right}\).
 6 months ago
 6 months ago
theEric Group Title
Hi! I'm looking at an example from my book and I'm hoping somebody can explain this. It's in the first chapter, but I don't want to skip out on anything. Thanks! Here is the issue: My book says that \(\dfrac{dp/dt}{p900}=\dfrac{1}{2}\) where \(p\neq 900\). Theennn... "By the chain rule the left side of [that equation] is the derivative of \(\ln\leftp900\right\) with respect to \(t\), so we have \(\dfrac{d}{dt} \ln\left p900\right=\dfrac{1}{2}\)" My issue is that I'm missing something. I see that \(\cancel{\dfrac{d}{dt}\dfrac{1}{p900}= \ln \left p900\right}\).
 6 months ago
 6 months ago

This Question is Closed

theEric Group TitleBest ResponseYou've already chosen the best response.0
I know the chain rule, like if \(f=f(g(t))\) then \(\dfrac{df}{dt}=\dfrac{df}{dg}\dfrac{dg}{dt}\). I think I'm just getting confused from looking at this too much...
 6 months ago

theEric Group TitleBest ResponseYou've already chosen the best response.0
I crossed that out because it's really \(\dfrac{1}{p900}=\dfrac{d}{dt}\ln\left p900\right\)
 6 months ago

theEric Group TitleBest ResponseYou've already chosen the best response.0
And so comes my problem... The book says that \(\dfrac{dp/dt}{p900}=\dfrac{1}{2}\) and \(\dfrac{d}{dt}\ln\leftp900\right = \dfrac{1}{2}\) Which means that \(\dfrac{dp/dt}{p900}=\dfrac{d}{dt}\ln\leftp900\right \) And I think that \(\dfrac{1}{p900}=\dfrac{d}{dt}\ln\leftp900\right \) I can't be right unless \(\dfrac{dp/dt}{p900}=\dfrac{1}{p900}\). This would imply that \(dp/dt=1\), which isn't necessarily true for this problem, that I see.
 6 months ago

theEric Group TitleBest ResponseYou've already chosen the best response.0
I said that I think \(\dfrac{1}{p900}=\dfrac{d}{dt}\ln\leftp900\right\), but really \(\dfrac{1}{p900}=\dfrac{d}{dp}\ln\leftp900\right\).
 6 months ago

theEric Group TitleBest ResponseYou've already chosen the best response.0
So then.... \(\dfrac{dp/dt}{p900}=\dfrac{dp}{dt}\dfrac{d}{dp}\ln\leftp900\right\)
 6 months ago

theEric Group TitleBest ResponseYou've already chosen the best response.0
\(\dfrac{dp}{dt}\dfrac{d}{dp}\longrightarrow\dfrac{d}{dt}\)
 6 months ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.