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Math Help - first principle derivative question

  1. #1
    Senior Member euclid2's Avatar
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    first principle derivative question

    find the derivative of \frac{4}{x+1} using first principles

    \frac {f(x+h)-f(x)}{h} = \frac {4}{(x+h)+1} - \frac{4}{x+1} * \frac{1}{h}

    this is as far as i can get i know to find a common demon i just can't get the right answer
    Last edited by euclid2; August 8th 2010 at 09:16 AM.
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  2. #2
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    Quote Originally Posted by euclid2 View Post
    find the derivative of \frac{4}{x+1} using first principles

    \frac {f(x+h)-f(x)}{h} = \frac {4}{(x+h)+1} - \frac{4}{x+1} * \frac{1}{h}

    this is as far as i can get i know to find a common demon i just can't get the right answer
    \displaystyle\huge\ f(x+h)-f(x)=\frac{4}{x+1+h}-\frac{4}{x+1}=\left(\frac{x+1}{x+1}\right)\frac{4}  {x+h+1}-\left(\frac{x+h+1}{x+h+1}\right)\frac{4}{x+1}

    \displaystyle\huge=\frac{4(x+1)-4(x+h+1)}{(x+1)(x+h+1)}=-4\frac{h}{(x+1)(x+h+1)}

    Now it's convenient to divide by "h" so next find

    \displaystyle\huge\frac{f(x+h)-f(x)}{h}

    Then take the limit by setting "h" to zero.
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