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Math Help - Implicit Differentiation

  1. #1
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    Implicit Differentiation

    Hi, I need some help with ^. I kind of feel embarrassed asking this question because it seems so easy. (I'm not sure if this belongs in Calc or PreCalc. I'm in PreCalc, but differentiation is Calc right?)

    The problem is x^3+y^3=125

    I want to find dy/dx, and the answer choices are

    a. [tex]-x/y[/Math]
    b. -x/5y
    c. y/x
    d. x/(y-5)
    e. x/y

    Well, my reasoning is that it should be -(x/y)^2, but it's not on the answer choices. It should also be negative and be devoid of the 5's right? Well, when left with -x/y ( dy/dx of x^2+y^2=C)

    Am I approaching the problem wrong or am I misunderstanding implicit differentiation.
    Last edited by FragKrag; October 21st 2008 at 07:52 PM. Reason: math tags!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by FragKrag View Post
    Hi, I need some help with ^. I kind of feel embarrassed asking this question because it seems so easy. (I'm not sure if this belongs in Calc or PreCalc. I'm in PreCalc, but differentiation is Calc right?)

    The problem is x^3+y^3=125

    I want to find dy/dx, and the answer choices are

    a. -x/y
    b. -x/5y
    c. y/x
    d. x/(y-5)
    e. x/y

    Well, my reasoning is that it should be -(x/y)^2, but it's not on the answer choices. It should also be negative and be devoid of the 5's right? Well, when left with -x/y ( dy/dx of x^2+y^2=C)

    Am I approaching the problem wrong or am I misunderstanding implicit differentiation.
    Yes, it would be -\left(\frac{x}{y}\right)^2

    The answer would have been (a) if the question was to implicitly differentiate x^{{\color{red}2}}+y^{{\color{red}2}}=125...

    --Chris
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