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Math Help - Simplifying derivatives

  1. #1
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    Simplifying derivatives

    Trying to find the derivative and I am stuck on simplifying it.

    What do I do after this step?
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  2. #2
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    Re: Simplifying derivatives

    Quote Originally Posted by minneola24 View Post
    Trying to find the derivative and I am stuck on simplifying it.

    What do I do after this step?
    Multiply by \frac{2\sqrt{x}}{2\sqrt{x}}.
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  3. #3
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    Re: Simplifying derivatives

    Doesn't that just move the \sqrt{x} to the denominator?

    I would combine the terms in the numerator and multiply by \frac{2}{2} to get the \frac{1}{2} out of the numerator.

    - Hollywood
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    Re: Simplifying derivatives

    Quote Originally Posted by hollywood View Post
    Doesn't that just move the \sqrt{x} to the denominator?

    What wrong with that?
    In fact, I is the form I required from students.
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  5. #5
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    Re: Simplifying derivatives

    Oops - I was reading x^{\frac{1}{2}} where it clearly said x^{-\frac{1}{2}}.

    The correct original expression is:

    \frac{(x^3+1)(\frac{1}{2}x^{-\frac{1}{2}})-(x^{\frac{1}{2}})(3x^2)}{(x^3+1)^2}

    which can be multiplied by \frac{2\sqrt{x}}{2\sqrt{x}} (as you said) to get

    \frac{1-5x^3}{2\sqrt{x}(x^3+1)^2}.

    (unless I've made another mistake.....)

    Thanks,
    Hollywood
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