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Math Help - fucction that I don't know how to differentiate

  1. #1
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    fucction that I don't know how to differentiate

    Differentiate the following function.


    g ' (u) =


    [LEFT]Attempt
    I don't know how I got it wrong this time
    I did
    = 3u^(1/2)+2u^(1/2)
    = 1.5u^(-1/2)+u(-1/2)
    = (3/2)u^(-1/2)+u^(-1/2)
    = 1/(3/2)u^(1/2)+1/(u^(1/2)
    = 1/(sqrt(3/2)u) + 1/(sqrt(u))

    I just learnt that x^-1/2 = 1/x^1/2

    I don't understand what I did wrong this time Please help me out! thank you so much!
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  2. #2
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    Quote Originally Posted by miss.strw View Post
    Differentiate the following function.


    g ' (u) =


    [LEFT]Attempt
    I don't know how I got it wrong this time
    I did
    = 3u^(1/2)+2u^(1/2)
    = 1.5u^(-1/2)+u(-1/2)
    = (3/2)u^(-1/2)+u^(-1/2)
    = 1/(3/2)u^(1/2)+1/(u^(1/2)
    = 1/(sqrt(3/2)u) + 1/(sqrt(u))

    I just learnt that x^-1/2 = 1/x^1/2

    I don't understand what I did wrong this time Please help me out! thank you so much!
    Re-write the term of the function:

    g(u)=\dfrac1{\frac{\sqrt{3}}2 u} + \dfrac1{\sqrt{u}} = \dfrac2{\sqrt{3}} \cdot u^{-1} + u^{-\frac12}

    Then

    g'(u)=(-1) \cdot \dfrac2{\sqrt{3}} \cdot u^{-2} - \dfrac12 \cdot u^{-\frac32}

    That's the first rough version of the derivate. You can simplify this term, so go ahead!
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