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Math Help - Finding the derivative of the function

  1. #1
    Member purplec16's Avatar
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    Finding the derivative of the function

     f(x)= \frac{{x}^{3 }-{4x}^{2 }+3 }{x }

    f'(x)=\f{3x}^{2 }-8x +{x}^{ -2}

    I'm kinda confused on what happens to the x in the denominator i don't know if i should add it or multiply the numerator by it so that is the answer i felt most comfortable
    Last edited by purplec16; May 24th 2011 at 03:50 PM. Reason: additional comment
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  2. #2
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    There are two ways to solve it. Either write it as you have and use the quotient rule. Or you can simply use f(x)=\frac{x^3-4x^2+3}{x}=x^2-4x+\frac{3}{x}
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  3. #3
    Member purplec16's Avatar
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    I really dont understand how you got that answer
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  4. #4
    Member purplec16's Avatar
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    oh ok cool thanks...i understand what you did you divided each term by x
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  5. #5
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    I just wrote f(x) in a different way using basic algebra. You should easily be able to differentiate the second form.
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  6. #6
    Member purplec16's Avatar
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    so is the answer f'(x) = 2x-8x-{3x}^{-2 }
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  7. #7
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    Almost, but the second term is not right.
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  8. #8
    Member purplec16's Avatar
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    so the answer is:

    f'(x)=2x-8-{3x}^{-2 }
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  9. #9
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    No. \frac{d}{dx}\left(-4x\right) \neq -8
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  10. #10
    Member purplec16's Avatar
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    sorry -4
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