Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    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


    User Avatar
    Science Advisor

    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


    User Avatar

    Staff: Mentor

    (thread moved to Calculus & Beyond)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook