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Math Help - Difference Quotient

  1. #1
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    Difference Quotient

    I'm new to calculus and haven't had pre-calc. I have a question regarding a certain problem.

    I'm to compute the derivative of a given function using the difference quotient.

    This is the function: f(x)= -2/x

    I only got as far as plugging the function into the formula before I got lost. Can someone please help?
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  2. #2
    Super Member
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    Israel
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    Quote Originally Posted by gstyzzer View Post
    I'm new to calculus and haven't had pre-calc. I have a question regarding a certain problem.

    I'm to compute the derivative of a given function using the difference quotient.

    This is the function: f(x)= -2/x

    I only got as far as plugging the function into the formula before I got lost. Can someone please help?
    Let f(x) = \frac{-2}{x}, then:

    \frac{df}{dx} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = \lim_{h \to 0} \frac{\frac{-2}{x+h} - \frac{-2}{x}}{h}  = \lim_{h \to 0} \frac{\frac{-2x}{x(x+h)} + \frac{2(x+h)}{x(x+h)}}{h}

    Can you finish it off from here? (Rest is in the spoiler.)

    Spoiler:
     \lim_{h \to 0} \frac{-2x +2x +2h}{hx(x+h)} = \lim_{h \to 0} \frac{2}{x(x+h)} = \lim_{h \to 0} \frac{2}{x^2+xh} = \frac{2}{x^2}
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  3. #3
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    Lesotho
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    Smile

    here is your solution so try to follow it

    f'(x)=g(x)h'(x)-h(x)g'(x)
    [g(x)]^2

    let -2=h(x) and x=g(x)
    f(x)=h(x)/g(x)

    f'(x)={xd(-2)-(-2)d(x)}/(x)^2
    dx d(x)
    =0+2
    x^2
    =2/x^2
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