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Math Help - Differentiation 4/x^-2

  1. #1
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    Differentiation 4/x^-2

    Hey guys, having a blank moment

    Could some one just give me an answer to the the derivative of 4/x^-2, the x to the power -2 has thrown me a bit , longer time since i did this i know it basic stuff , having one of those days
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  2. #2
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    Re: Differentiation 4/x^-2

    \frac{4}{x^{-2}} = 4x^2

    Now differentiate...
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  3. #3
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    Re: Differentiation 4/x^-2

    x^-2=1/x^2 So 4/x^-2= 4x^2 whose derivative=8x
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  4. #4
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    Re: Differentiation 4/x^-2

    The hard way, using the "quotient rule": (f/g)'= (f'g- fg')/g^2 with f= 4, a constant so f'= 0, and g= x^{-2} so g'= -2x^{-3}. (4/x^2)'= [(0)(x^{-2})- (4)(-2x^{-3}]/x^{-4}= 8x^{-3}/x^{-4}= 8x^{-3-(-4)}= 8x

    Gosh, wasn't that fun!
    Last edited by HallsofIvy; June 15th 2012 at 09:44 AM.
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  5. #5
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    Re: Differentiation 4/x^-2

    Quotient rule, boo...lol

    \frac{d}{dx} \frac{4}{x^{-2}} = \frac{d}{dx} 4x^2 = 8x
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