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Math Help - differentiation question

  1. #1
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    differentiation question

    Hello, I am having trouble understanding how to differentiate this polynominal.
    Can someone please outline the steps. I want to use the Newton and Leibniz method rather than the first principles formuls.
    Thanks kindly for any help.

    4√x +4/x
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  2. #2
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    \displaystyle 4\sqrt{x} + \frac{4}{x} = 4x^{\frac{1}{2}} + 4x^{-1}.

    Now differentiate each term.
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  3. #3
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    thanks, I can get the second term, but still cannot get the correct answer for the first term (4√x).
    What is the answer for that first term ? Then I will be able to understand.

    Thanks

    (for the first term, I am getting 2/x^1/2, but I dont think that is correct.)
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  4. #4
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    \displaystyle \frac{d}{dx}\left(4x^{\frac{1}{2}}\right) = \frac{1}{2}\cdot 4x^{\frac{1}{2} - 1}

    \displaystyle = 2x^{-\frac{1}{2}}

    \displaystyle = \frac{2}{x^{\frac{1}{2}}}

    \displaystyle = \frac{2}{\sqrt{x}}.


    So you are correct.
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  5. #5
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    The first term (4√x)
    f`(x) = (1\2√x).4 = 2\√x

    The seconed term
    f`(4\x ) = (-1.4 )\ x^2 = -4\x^2
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