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Derivation Problem

  1. Sep 3, 2010 #1
    1. The problem statement, all variables and given/known data

    I dont manage to derive a function properly :(

    2. Relevant equations

    u = x^α * [(m-Ax)/B]^β

    3. The attempt at a solution

    FOC: x^α*ln(x)*????=0

    It is the second factor I have a problem with. Preciate any help!
  2. jcsd
  3. Sep 3, 2010 #2


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    Homework Helper

    Are you sure this is precalculus? Because it is not nearly as simple as you seem to think it should be.
    Let me assume that your variable is x and that all other letters represent constants.

    Then first of all, there are two functions of x being multiplied, so you will need the product rule:
    (xα * [(m-Ax)/B]β)' = (xα)' * [(m-Ax)/B]β + xα * ( [(m-Ax)/B]β )'
    Then the derivative of xα is not xα ln(x), but if x is the variable it's simply α xα - 1. For the derivative of the second part, you will need the chain rule (you can write it as yβ and get β yβ - 1 dy/dx).

    If, for some strange reason, you want to take the derivative with respect to α, however, you are right: you simply get
    x^α ln(x) * [(m-Ax)/B]^β
    because the whole second factor is simply constant with respect to α.
  4. Sep 3, 2010 #3


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    The natural logarithm only turns up in derivatives of exponential problems, such as the derivative of [itex]a^x[/itex]- that is, with the variable, x, in the exponent.

    Problems like this, which is just a power of x, with x in the base, are done by the 'power law', [itex](x^a)'= ax^{a- 1}[/itex] which is true for a and number, not just integers.
  5. Sep 3, 2010 #4


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    Staff: Mentor

    (thread moved to Calculus & Beyond)
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