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    rusticoroad's Avatar
    rusticoroad Posts: 2, Reputation: 1
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    #1

    Mar 9, 2011, 07:10 AM
    Derivative
    I have a derivative question.
    If "p" is price and "q" is quantity, and the demand for a product is q = 5000e(-0.08p) (exponential function), what is the derivative of demand with respect to price when p=$10. Interpret answer in terms of demand.
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    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Mar 9, 2011, 07:26 AM

    The derivative of a function like



    is:



    For your function you have p as the independent variable rather than x, A = 5000 and b = -0.08. Can you finish it from here?
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    rusticoroad Posts: 2, Reputation: 1
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    #3

    Mar 9, 2011, 08:03 AM
    Comment on ebaines's post
    I thought that the answer might be: q'= -400e (-.08 x 10) = -179.73. Am I doing the derivative wrong?
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    ebaines Posts: 12,131, Reputation: 1307
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    #4

    Mar 9, 2011, 08:16 AM

    Please do not use the comment feature of the web site to ask follow-up questions, but rather use the "answer" box.

    You have it correct: the derivative at p = 10 is indeed dp/dq = -179.73 units/dollar.
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