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Math Help - Differentiation problem

  1. #1
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    Differentiation problem

    ax1a-1x21-a/(1-a)x1ax2-a = p1/p2



    Hey guys. Stuck with this problem as I have forgotten my differentiation rules. I want to be able to show how to cancel down the equation so that it reads

    a/(1-a) . x2/x1 = p1/p2

    It would be great if someone could give me a step by step breakdown and remind me which rules I need to use here. Thank you

    (sorry I didnt know how to use the mathematical script)
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  2. #2
    Behold, the power of SARDINES!
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    Re: Differentiation problem

    Quote Originally Posted by oh507 View Post
    ax1a-1x21-a/(1-a)x1ax2-a = p1/p2



    Hey guys. Stuck with this problem as I have forgotten my differentiation rules. I want to be able to show how to cancel down the equation so that it reads

    a/(1-a) . x2/x1 = p1/p2

    It would be great if someone could give me a step by step breakdown and remind me which rules I need to use here. Thank you

    (sorry I didnt know how to use the mathematical script)
    It is not a derivative rule you need, but the law of exponents.

    \frac{a^{m}}{a^n}=a^{m-n} and a^{-m}-\frac{1}{a^m}

    So you have

    \frac{ax_{1}^{a-1}x_{2}^{1-a}}{(1-a)x_1^{a}x_2^{-a}}=\frac{ax_{1}^{-1}x_2^{-1}}{(1-a)}=\frac{a}{(a-1)x_1x_2}
    Last edited by TheEmptySet; November 1st 2012 at 04:39 AM. Reason: typo
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  3. #3
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    Re: Differentiation problem

    Hi oh507,

    For this problem you don't need any differentiation rules. You need the rules about exponents to simplify the equation. Specifically you will need:

    x^{m} x^{n} = x^{m+n}

    and

    x^{-m} = \frac{1}{x^{m}}

    or

    \frac{1}{x^{-m}} = x^{m}

    to simplify your equation.
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  4. #4
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    Re: Differentiation problem

    Ok, will relearn my rules and try figure out for myself. Thanks a lot!
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