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Homework Help: Derivative of exponential functions

  1. Sep 5, 2008 #1
    1. The problem statement, all variables and given/known data

    d/dT (e-E0/(kT))

    2. Relevant equations

    d/dx(ex) = ex

    3. The attempt at a solution

    e-E0/(kT) * E0/kT2 ???

    Do you use the chain rule on the exponent of e?
  2. jcsd
  3. Sep 5, 2008 #2


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    Staff Emeritus
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    Looks spot on to me :approve:. And yes, you would use the chain rule (followed by the power rule on the exponent) to differentiate the function.
  4. Sep 5, 2008 #3
    if u=u(x),
    d/dx (e^u) = e^u du/dx
    d/dx (e^(1/x)) = e^(1/x) (-1)/(x^2)
    d/dx (e^(a/x)) = e^(a/x) (-a)/(x^2)
    d/dx (e^(a/bx)) = e^(a/bx) (-a/b)/(x^2)
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