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Math Help - More Differentiation Questions

  1. #1
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    More Differentiation Questions

    I guess i should first ask, is it proper form here to start new threads or edit my old ones... either way, i'll post in this new one for now.

    Trying to work out y' of the square root of x-1 / x+1 (all terms inside the root, didnt know how to indicate that in text)

    I assume that I make it (x-1 / x+1)^1/2 but i get into a very tangly equation when I use the quotient rule. Is this the right way to start here?
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  2. #2
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    Have to use chain rule and quotient rule.

    y = sqrt(x-1 / x+1)
    y = (x-1 / x+1)^0.5
    dy/dx = 0.5(x-1 / x+1)^-0.5 multiply d/dx(x-1/x+1)

    Can you take it from here ?

    Quote Originally Posted by timmy420 View Post
    I guess i should first ask, is it proper form here to start new threads or edit my old ones... either way, i'll post in this new one for now.

    Trying to work out y' of the square root of x-1 / x+1 (all terms inside the root, didnt know how to indicate that in text)

    I assume that I make it (x-1 / x+1)^1/2 but i get into a very tangly equation when I use the quotient rule. Is this the right way to start here?
    Last edited by tester85; December 10th 2008 at 09:47 PM.
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  3. #3
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    i got the chain rule part, but im getting tangled up in the algebra i think.

    I multiply .5(x-1/x+1)^.5 by the derrivitive which i worked out to be 2/(x+1)^2 and get confused.
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  4. #4
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    y = sqrt(x-1 / x+1)
    y = (x-1 / x+1)^0.5
    dy/dx = 0.5(x-1 / x+1)^-0.5 multiply d/dx(x-1/x+1)
    dy/dx = 1/2(x-1 / x+1)^-1/2 multiply ((x+1)(1) - (x-1)(1) / (x+1)^2)
    dy/dx = 1/2(sqrt(x+1)/sqrt(x-1)) multiply 2 / (x+1)^2
    dy/dx = sqrt(x+1)/sqrt(x-1)(x+1)^2
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  5. #5
    Newbie Msquared's Avatar
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    You can always use synthetic or long division to reduce the equation inside the radical to:

    1- (2)/(x+1)

    Makes it a little more bearable to derive and you no longer have to worry about applying the quotient rule to the interior of the radical.
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