1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Differentiation / Chain rule

  1. May 16, 2017 #1
    1. The problem statement, all variables and given/known data

    holdmeinurpantaloonies.png
    Use the top line to get 1) and 2)

    2. Relevant equations
    above
    3. The attempt at a solution
    So for 2) split the log up using ##log (AB)=log (A) + log (B) ## and this is simple enough

    I think I may be doing something stupid with 1) though. I have

    ##\frac{\partial}{\partial \tau} log (\eta(\frac{-1}{\tau})) = \frac{\partial}{\partial \tau} log (\eta(\tau)) \frac{\partial}{\partial \tau}(\frac{-1}{\tau})= \frac{1}{\tau^2} \frac{ \pi i}{12} E_2(\tau)##
     
  2. jcsd
  3. May 16, 2017 #2
    ##(f(g(x)))^\prime = f^\prime(g(x))g^\prime(x)##

    You applied the rule incorrectly,

    ##\displaystyle \frac{\partial}{\partial \tau} log (\eta(\frac{-1}{\tau})) = \frac{\partial}{\partial \tau} log (\eta(\color{red}{\frac{-1}{\tau}})) \frac{\partial}{\partial \tau}(\frac{-1}{\tau})= \frac{1}{\tau^2} \frac{ \pi i}{12} E_2(\color{red}{\frac{-1}{\tau}})##
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...