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Math Help - Tough derivative

  1. #1
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    Tough derivative

    Find the derivative of the function.



    I keep on getting a weird answer and I don't think its correct. Sorry that I don't know how to write latex.

    y'(x)= 1/2(11+sqrt11+sqrt11)^-1/2 [1+11/2(11+sqrt11)^-1/2 (1+ 11/2x^-1/2)]

    Any help is appreciated
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  2. #2
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    <br />
\frac{\frac{\frac{\sqrt{11}}{2\sqrt{x}}+11}{2\sqrt  {11x+\sqrt{11}\sqrt{x}}}+11}{2\sqrt{11x+\sqrt{11x+  \sqrt{11}\sqrt{x}}}}<br />
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by rodjav305 View Post
    Find the derivative of the function.



    I keep on getting a weird answer and I don't think its correct. Sorry that I don't know how to write latex.

    y'(x)= 1/2(11+sqrt11+sqrt11)^-1/2 [1+11/2(11+sqrt11)^-1/2 (1+ 11/2x^-1/2)]

    Any help is appreciated
    y=\sqrt{ax+\sqrt{ax+\sqrt{ax}}}\implies y^2-ax= \sqrt{ax+\sqrt{ax}}\implies \left(y^2-ax\right)^2=y^4-2y^2ax+1= ax+\sqrt{ax}. Thus, 4y^3y''+2yy'ax+2ya=a+\frac{\sqrt{a}}{2\sqrt{x}}. Doing a little finagling we get y'=\frac{a-\frac{\sqrt{a}}{2\sqrt{x}}-2ya}{4y^3+2ax}. Therefore y'=\frac{a-\frac{\sqrt{a}}{2\sqrt{x}}-2a\sqrt{ax+\sqrt{ax+\sqrt{ax}}}}{4\left(ax+\sqrt{a  x+\sqrt{ax}}\right)^{\frac{3}{2}}+2ax}
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  4. #4
    Super Member bigwave's Avatar
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    from the wolf..

    you might want to look at this:

    derivative of &#x28;sqrt &#x28;11x &#x2b; &#x28;sqrt &#x28;11x &#x2b;&#x28;sqrt 11x - Wolfram|Alpha)))))

    I am too slow with latex...
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  5. #5
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    I would first square both sides of the equation and then take the derivative.
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  6. #6
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    Thank you to everyone, by the way thanks for the link the program does a very clear cut explanation
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