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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

    Mark44

    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

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    If y = c * f(x), then dy/dx = c * d[f(x)]/dx
     
    Last edited: Jun 25, 2013
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