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Math Help - derivatives

  1. #1
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    derivatives

    I need to find the derivative of y = sqrt(x-1), using the derivative formula f(x + h) - f(x) / h

    At the moment I have sqrt((x+h) -1) - sqrt(x-1) / h

    I tried multiplying the top and bottom by the conjugate but it didn't work.
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  2. #2
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    Quote Originally Posted by steezin View Post
    I need to find the derivative of y = sqrt(x-1), using the derivative formula f(x + h) - f(x) / h

    At the moment I have sqrt((x+h) -1) - sqrt(x-1) / h

    I tried multiplying the top and bottom by the conjugate but it didn't work.
    it didn't? ...


    \frac{\sqrt{x+h-1} - \sqrt{x-1}}{h} \cdot \frac{\sqrt{x+h-1} + \sqrt{x-1}}{\sqrt{x+h-1} + \sqrt{x-1}}

    \frac{(x+h-1) - (x-1)}{h(\sqrt{x+h-1} + \sqrt{x-1})}

    \frac{h}{h(\sqrt{x+h-1} + \sqrt{x-1})}

    \frac{1}{\sqrt{x+h-1} + \sqrt{x-1}}

    now take the limit as h \to 0
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  3. #3
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    Thank you so much, turns out I mixed up one of the signs lol
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