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Math Help - Differentiation

  1. #1
    Newbie
    Joined
    Feb 2009
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    17

    Differentiation

    The problem is to determine where the function is increasing, decreasing, concave up and concave down.

    1) y=(2x-3)^(1/3)

    2) y=1/(1+e^-x)

    for the first one, i got the first derivative of (1) 2/3(2x-3)^(-2/3)
    but im not sure if this is right.
    and i have no idea for the second derivative.
    and i really really have no idea for the second problem.
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  2. #2
    Member
    Joined
    May 2008
    Posts
    106
    Your first derivative is right!

    for the second just differentiate your expression for the first derivative again, you used the chain rule for the first I'm guessing so just use it again.

    I get

    <br />
\frac{d^2y}{dx^2}=-\frac{8}{9}(2x-3)^{-\frac{5}{3}}<br />

    For the second one rewrite it as

    <br />
y=(1+e^{-x})^{-1}<br />

    then use the chain rule

    I get \frac{e^{-x}}{(1+e^{-x})^2}

    Then use the quotient rule on this to get the second derivative
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