August 4th, 2018, 03:48 PM  #1 
Newbie Joined: Jun 2017 From: italia Posts: 13 Thanks: 2  a = f(n), da/dt = f(dn/dt)
Let $a^3 = \frac{10096.676}{n^2}$. I know $a$, $n$ and $dn/dt$. Is there any way to calculate $da/dt$? 
August 4th, 2018, 04:50 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,913 Thanks: 1113 Math Focus: Elementary mathematics and beyond 
Differentiate implicitly $$3a^2\frac{da}{dt}=\frac{20193.352}{n^3}\frac{dn}{dt}$$ and solve for $\frac{da}{dt}$. 
August 5th, 2018, 03:29 AM  #3 
Newbie Joined: Jun 2017 From: italia Posts: 13 Thanks: 2 
Do you mean $$\frac{da}{dt}=\frac{\frac{20193.352}{n^3}\frac{dn}{dt}}{3a^2}$$ ? The result seems good and the dimensional analysis is good (it's an astronomy problem). I should be reasonably sure that the formula I wrote in my program is correct. Thanks a lot! Last edited by Cristiano; August 5th, 2018 at 03:33 AM. 
August 5th, 2018, 05:07 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,913 Thanks: 1113 Math Focus: Elementary mathematics and beyond 
That's it and you're welcome.
