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Thread: Calculus Derivative HELP! Please

  1. #1
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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. #2
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    Hello, Casas4!

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


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

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

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

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


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

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