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Math Help - Derivative question?

  1. #1
    Member nautica17's Avatar
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    Derivative question?

    d/dx (x^2 + 1)/x

    I need to solve this without quotient rule. Power rule is the most I can use on this problem. The only thing is that I don't see how to get the answer correctly. With quotient rule I can do this but I'm having troubles doing this purely algebraically and with power rule only.

    I've tried doing (x^2 + 1)*x^-1, but that gives me 1 as my answer, (which I know is incorrect).

    So the answer that Wolfram Alpha is spitting out is 2-((x^2 + 1)/x) , but if I do quotient rule, I get (x^2 - 1)/x^2. So both answers are technically correct, and I think the first one is the one probably possible by algebra.

    So can someone push me a step or two in the right direction. I want to solve this so badly. >.< But I have no clue where to start anymore since I've tried several methods to no avail.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    f = (x^2 + 1)/x = x +1/x

    f ' = 1 - 1/x^2 = (x^2 -1)/x^2
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  3. #3
    Member nautica17's Avatar
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    Quote Originally Posted by Calculus26 View Post
    f = (x^2 + 1)/x = x +1/x

    f ' = 1 - 1/x^2 = (x^2 -1)/x^2
    Thank-you!
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