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Math Help - Derivative value and point finding

  1. #1
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    Derivative value and point finding

    Can someone show me how to find the value of the derivative of the function at the given point :

    g(x)=\frac{4x-5}{x^2-1} at the point (0,5)


    Thank you!
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  2. #2
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    Use the quotient rule.

    If y(x)=\frac{g(x)}{h(x)} then y'(x)=\frac{g'(x)h(x)-g(x)h'(x)}{[h(x)]^2}
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  3. #3
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    I really don't mean to be a pest, but could you go a bit further and show me how I'g plug in these variables. All this is pretty new to me (I know that's a terrible excuse) ... Sorry. :/ I'm having a lot of trouble with this stuff.
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  4. #4
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    y(x)=\frac{4x-5}{x^2-1}<br />

    Let g(x)=4x-5 and h(x)=x^2-1

    Then g'(x)=4 and h'(x)=2x

    Plug this into the formula above and you get:

    y'(x)=\frac{g'(x)h(x)-g(x)h'(x)}{[h(x)]^2}=\frac{4(x^2-1)-2x(4x-5)}{(x^2-1)^2}=...

    At the point (0,5), the x value is 0, so just plug in 0 instead of x into the derivative.
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