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Math Help - differentiating a function from first principles

  1. #1
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    differentiating a function from first principles

    lim ((x+h)^-2 - x^-2)/h as h->0 - Wolfram|Alpha

    I don't know where the answer is coming from. What are the missing steps?
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  2. #2
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    Re: differentiating a function from first principles

    I have found I have done this question before. It involves making a common denominator.
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  3. #3
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    Re: differentiating a function from first principles

    Quote Originally Posted by Stuck Man View Post
    lim ((x+h)^-2 - x^-2)/h as h->0 - Wolfram|Alpha

    I don't know where the answer is coming from. What are the missing steps?
    Try getting a common denominator, then expanding the numerator...
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  4. #4
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    Re: differentiating a function from first principles

    \lim_{h \to 0} \frac{\frac{1}{(x+h)^2} - \frac{1}{x^2}}{h}

    \lim_{h \to 0} \frac{\frac{1}{(x+h)^2} - \frac{1}{x^2}}{h} \cdot \frac{x^2(x+h)^2}{x^2(x+h)^2}

    \lim_{h \to 0} \frac{x^2 - (x+h)^2}{h \cdot x^2(x+h)^2}

    finish it ...
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