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Math Help - Chain rule help

  1. #1
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    Chain rule help

    the question is find dy/dx at the indicated value of x

    y = sqrt[u^2 +5], where u = (1-x)/(1+x) ; x=-2

    the answer the book has is 6/sqrt14 but I am getting 3/sqrt14

    here is my work

    1/2[u^2 + 5]^(-1/2) * 2u * d/dx(u)

    comes down to [1/2] * 14^(-1/2) * (-6) * (-1)

    giving me 6/2sqrt14 -> 3/sqrt14

    thank you!
    Last edited by Jonroberts74; October 3rd 2013 at 09:13 PM.
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  2. #2
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    Re: Chain rule help

    First I'll try to retype your given equations.

     y =\sqrt{u^2+5} \quad \text{ and }  \quad u=\frac{1-x}{1+x} \\ \frac{dy}{dx}=\frac{2u}{2\sqrt{u^2+5}}\frac{du}{dx  }=\frac{u}{\sqrt{u^2+5}}\frac{du}{dx} \quad \text{ and } \quad \\ \frac{du}{dx}=\frac{(-1)(1+x)+(-1)(1-x)}{(1+x)^2}=\frac{-2}{(1+x)^2}

    Try to plug in u and du/dx into dy/dx
    Thanks from Jonroberts74
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  3. #3
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    Re: Chain rule help

    oh, I was forgetting the quotient rule. thank you
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