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Math Help - derivative as a limit problem

  1. #1
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    Question derivative as a limit problem

    Use the definition of derivative as a limit to find the derivative of
    {x}/{(x+1)}

    show me all steps please, thank you!
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by melody View Post
    Use the definition of derivative as a limit to find the derivative of
    {x}/{(x+1)}

    show me all steps please, thank you!
    \frac{\frac{x+h}{x+h+1}-\frac{x}{x+1}}{h}=\frac{\frac{(x+h)(x+1)}{(x+h+1)(  x+1)}-\frac{x(x+h+1)}{(x+1)(x+h+1)}}{h} =\frac{\frac{x^2+hx+x+h-(x^2+hx+x)}{(x+1)(x+h+1)}}{h}=\frac{\frac{h}{(x+1)  (x+h+1)}}{h}=\frac{1}{(x+1)(x+h+1)}

    Taking the limit as h\to0, we have:

    \lim_{h\to0}\frac{1}{(x+1)(x+h+1)}=\frac{1}{(x+1)^  2}
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