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: Hyperbolic function and the product rule.

  1. Jun 24, 2013 #1
    1. The problem statement, all variables and given/known data

    The question I am trying to answer requires me to find the following:

    dN/dS ∝ S^−5/2/cosh(r/R)

    and I am giving the follwing equation in the question.

    A=4πR^2 sinh^2⁡〖(r/R)〗

    3. The attempt at a solution

    Right I know how to get the S^-5/2 in the top half of the equation.

    I also understand that the cosh part comes from the differentiation of A. The problem I have is after applying the product rule to A I end up with this:

    dA/dr=8πRsinh^2 (r/R)+ 8πR^2 sinh⁡(r/R)cosh⁡(r/R)

    I am stuck on how the terms cancel to leave me with cosh(r/R) so i can reach the equation required.
  2. jcsd
  3. Jun 24, 2013 #2


    Staff: Mentor

    The product rule doesn't apply here, but the chain rule does. The factor 4πR2 is considered to be a constant as far as differentiation with respect to r is concerned.
  4. Jun 25, 2013 #3
    Ah, I see. So applying the chain rule with respect to r would mean that 4πR^2 would disappear because the derivative of a constant is zero?
  5. Jun 25, 2013 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    If y = c * f(x), then dy/dx = c * d[f(x)]/dx
    Last edited: Jun 25, 2013
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted