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Math Help - Derivative

  1. #1
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    Derivative

    Hi.
    How to find the derivative of 1/(x^2) using definition of the derivative;I know how to find it by using the power rule but not the definition.




    Thanks.
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  2. #2
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    The definition of the derivative is: If f(x) = \frac{1}{x^2} then
     f'(x) = \lim_{h\to 0} \frac{f(x+h) - f(x)}{h}
    So try doing that and come back and tell us how you did. We can help you if you still need help.
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  3. #3
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    I need a hint, 'cause I'm still stuck.
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  4. #4
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    Tell me what f(x+h) and f(x) are, then tell post what \frac{f(x+h) - f(x)}{h}. Once you have all that you should be able to simplify things and take the derivative.
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  5. #5
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    \displaystyle f'(x) = \lim_{h \to 0} \frac{\frac{1}{(x+h)^2} - \frac{1}{x^2}}{h}

    start by getting a common denominator and get those two fractions in the numerator together.
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  6. #6
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    I keep getting lost during simplifying process.(what's wrong with me)
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  7. #7
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    Quote Originally Posted by wowo View Post
    I keep getting lost during simplifying process. what's wrong with me
    can' say ... you haven't shown anything other than posting the problem.

    start by getting these two fractions together ...

    \displaystyle \frac{1}{(x+h)^2} - \frac{1}{x^2}

    ... note that the common denominator is x^2(x+h)^2.

    do it.
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  8. #8
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    x^2-1(x^2+2xh+h^2)/(x^2+2xh+h^2)(x^2)/h

    Am I right????
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  9. #9
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    Yes, continue simplification. Eventually an h will cancel.
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  10. #10
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    Quote Originally Posted by wowo View Post
    x^2-1(x^2+2xh+h^2)/(x^2+2xh+h^2)(x^2)/h

    Am I right????
    keep going ... clean it up
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  11. #11
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    Okay, I'm completely lost with simplifying
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  12. #12
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    Quote Originally Posted by wowo View Post
    Okay, I'm completely lost with simplifying
    \displaystyle \frac{1}{h} \left[\frac{x^2 - (x^2 + 2xh + h^2)}{x^2(x+h)^2}\right]

    distribute the negative in the numerator and combine like terms ... then factor out an  h from what's left in the numerator ...
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  13. #13
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    So, It's 2x+h/(x^2(x+h)^2
    2x/(x^2)(x^2)
    2/x^3
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  14. #14
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    Quote Originally Posted by wowo View Post
    So, It's 2x+h/(x^2(x+h)^2
    2x/(x^2)(x^2)
    2/x^3
    No. You have made a careless mistake in the numerator. Go back, check your work, find the mistake. Hint: You know what the final answer is meant to be, don't you ....?
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  15. #15
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    Is it -2x+h/(x^2(x+h)^2 ??
    Last edited by wowo; October 17th 2010 at 05:51 PM.
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