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Second derivative of an exponential function

  1. Jul 22, 2013 #1
    1. The problem statement, all variables and given/known data
    I have the derived function:
    f'(x) = [1/(1+kx)^2]e^[x/(1+kx)]
    k is a positive constant


    2. Relevant equations
    I need to find the second derivative, which I thought was just the derivative of the exponent multiplied by the coefficient (as you find the first derivative), but the answers say:

    f''(x) = [1/(1+kx)^4]e^[x/(1+kx)] + e^[x/(1+kx)] . [-2k/(1+kx)^3]

    3. The attempt at a solution
    All I managed to get was:
    f''(x) = [1/(1+kx)^4]e^[x/(1+kx)]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 22, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You say "I thought was just the derivative of the exponent multiplied by the coefficient (as you find the first derivative)...", but THAT is not true: it is true ONLY if the "coefficient" of the exponential is a constant. If the coefficient itself is a function of x it will not work. Go back and review some basic properties of derivatives.
     
  4. Jul 22, 2013 #3
    ##\frac{df}{dx}=\frac{e^{\frac{x}{1+kx}}}{(1+kx)^2}##. You have the quotient of two functions of ##x##. You can't just take the derivative of the exponential term. What do you do when you have a product or quotient of functions?
     
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