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Math Help - Differentiate a fraction

  1. #1
    Senior Member Mukilab's Avatar
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    Differentiate a fraction

    How would I differentiate this?

    x^2+\frac{2000}{x}

    I thought it would go like this (but it doesn't work). Where am I going wrong?::
    x^2+2000*x^{-1}>>>>> x^2+2000^{-1}*x^{-2}=x^2+\frac{1}{2000}*\frac{1}{x^2}

    Please help me out. Thank you in advance.
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Differentiate a fraction

    x^2+2000*x^{-1}>>>>>2* x - 2000*x^{-2}
    Thanks from Mukilab
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: Differentiate a fraction

    I would write the function as:

    f(x)=x^2+2000x^{-1}

    To differentiate, use the power rule term by term: \frac{d}{dx}\left(kx^r \right)=krx^{r-1}
    Thanks from Mukilab
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  4. #4
    Senior Member Mukilab's Avatar
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    Re: Differentiate a fraction

    Thanks guys
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  5. #5
    Senior Member Mukilab's Avatar
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    Re: Differentiate a fraction

    What something such as \frac{24300x-225x^3}{16}

    Surely since the 16^(-1) differentiates to 0, the whole equation differentiates to 0 (since everything is multiplied by 16^(-1))
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  6. #6
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    Re: Differentiate a fraction

    no ...

    \frac{d}{dx} \left[ c \cdot f(x)\right] = c \cdot f'(x)

    y = \frac{1}{16}(24300x - 225x^3)

    y' = \frac{1}{16}(24300 - 675x^2)


    fyi, problems involving derivatives belong in the calculus forum
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  7. #7
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Differentiate a fraction

    f'(x)=\frac{1}{16} \left(24300-675 x^2\right)
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  8. #8
    Senior Member Mukilab's Avatar
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    Re: Differentiate a fraction

    Quote Originally Posted by skeeter View Post
    no ...

    \frac{d}{dx} \left[ c \cdot f(x)\right] = c \cdot f'(x)

    y = \frac{1}{16}(24300x - 225x^3)

    y' = \frac{1}{16}(24300 - 675x^2)


    fyi, problems involving derivatives belong in the calculus forum
    Quote Originally Posted by MaxJasper View Post
    f'(x)=\frac{1}{16} \left(24300-675 x^2\right)
    Wow I was always told to multiply out before doing any differentiating. Thanks for that!
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  9. #9
    Senior Member Mukilab's Avatar
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    Re: Differentiate a fraction

    Can I do the same for integration? I.e. ignoring 15/16 until after I've integrated the thing in the brackets.
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  10. #10
    MHF Contributor
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    Re: Differentiate a fraction

    \int k \cdot f(x) \, dx = k \int f(x) \, dx


    look over your basic rules ... they're in your text.
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  11. #11
    Senior Member Mukilab's Avatar
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    Re: Differentiate a fraction

    Quote Originally Posted by skeeter View Post
    \int k \cdot f(x) \, dx = k \int f(x) \, dx


    look over your basic rules ... they're in your text.
    You would be surprised.

    How does one determine f(x)? Is it just anything involving an x? In other words, can I make anything k as long as it multiplies into the f(x) and does not involve x?
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  12. #12
    MHF Contributor
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    Re: Differentiate a fraction

    k is a constant factor of the function
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