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Math Help - Derivative, f(x) question

  1. #1
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    Derivative, f(x) question

    hi friends

    confused here. question is

    f(x) = x / (x-1) use the definition of the derivative to determine f ' (x)


    I know it has something to do with inverse functions but i dont know how to start.

    working as well please so i can follow what your doing

    thanks
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  2. #2
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    Re: Derivative, f(x) question

    Quote Originally Posted by Hooperoo View Post
    f(x) = x / (x-1) use the definition of the derivative to determine f ' (x)
    I know it has something to do with inverse functions but i dont know how to start.
    working as well please so i can follow what your doing
    As written, it has nothing to do with inverse.

    You find {\lim _{h \to 0}}\frac{{f(x + h) - f(x)}}{h}
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  3. #3
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    Re: Derivative, f(x) question

    Quote Originally Posted by Hooperoo View Post
    hi friends

    confused here. question is

    f(x) = x / (x-1) use the definition of the derivative to determine f ' (x)


    I know it has something to do with inverse functions but i dont know how to start.

    working as well please so i can follow what your doing

    thanks
    \displaystyle \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}=\displaystyle \lim_{h \to 0}\frac{\frac{x+h}{x+h-1}-\frac{x}{x-1}}{h}=\displaystyle \lim_{h \to 0} \frac{-1}{(x+h-1)(x-1)}=\frac{-1}{(x-1)^2}
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  4. #4
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    Re: Derivative, f(x) question

    oh poop, sorry bout the inverse thing. getting very confused about whats inverse and whats to do with limits. thank you both!!!
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