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Thread: Calculus Derivative HELP! Please

  1. October 14th 2008, 08:07 PM #1
    Casas4
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    Calculus Derivative HELP! Please

    Can some one help explain this to me i think i am suppose to the quotient rule to solve this.
    Consider the function h(x), for which h(4)=4 and h(prime)(4)=(-4) or the derivative of h^1(4)=(-4)
    Find F^1(4) for the function f(x)=(h(x))/(x)
    Hopefully i explained that right
    Thanks to anyone who can help
    AC
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  2. October 14th 2008, 08:22 PM #2
    Soroban
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    Hello, Casas4!

    By the way, the derivative is written: f'(x) ... " f prime" ... not f^1

    Consider the function h(x), for which h(4)=4 and h'(4)= \text{-}4

    Find f'(4) where: f(x)\:=\:\frac{h(x)}{x}

    We are given: . f(x) \:=\:\frac{h(x)}{x}

    Quotient Rule: . f'(x) \;=\;\frac{x\!\cdot\!h'(x) - h(x)}{x^2}


    Therefore: . f'(4) \;=\;\frac{4\!\cdot\!h'(4) - h(4)}{4^2} \;=\;\frac{4(\text{-}4) - 4}{16} \;=\;\frac{\text{-}20}{16} \;=\;\boxed{-\frac{5}{4}}
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