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Math Help - Differential Equations...

  1. #1
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    Differential Equations...

    Use the definition of the derivative to find f' (x).

    f (x)=  \frac {1}{x^2}

    f'(x)=  {\lim_{\Delta x \rightarrow 0}} \frac{\frac {1}{(x+ \Delta x)^2} - \frac {1}{x^2}} {\Delta x}

    Should I get a common denominator in the top of the problem?
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  2. #2
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    Quote Originally Posted by yeloc View Post
    Use the definition of the derivative to find f' (x).

    f (x)=  \frac {1}{x^2}

    f'(x)=  {\lim_{\Delta x \rightarrow 0}} \frac{\frac {1}{(x+ \Delta x)^2} - \frac {1}{x^2}} {\Delta x}

    Should I get a common denominator in the top of the problem?
    yes. you should get a common denominator in the top, and simplify the top of numerator.
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  3. #3
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    I got a common denominator of  x^4+2x^3 \Delta x+x^2 \Delta x^2

    So would the final answer be  \frac {-2x} {x^4} ?
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  4. #4
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    Quote Originally Posted by yeloc View Post
    I got a common denominator of  x^4+2x^3 \Delta x+x^2 \Delta x^2

    So would the final answer be  \frac {-2x} {x^4} ?
    The answer is correct but can be simplified.
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  5. #5
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     \frac {-2} {x^3} I knew I missed something. Thanks!
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