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Math Help - Real quick derivative answer and maybe explain?

  1. #1
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    Real quick derivative answer and maybe explain?

    Yesterday in my calc class I possed a derivative problem to my professor who spent 40 mins on the problem... burned all class and didnt come up with an answer so I ask you if you know.

    y=sqrt(x+sqrt(x+sqrt(x)))

    written differently y=(x+(x+(x)^(1/2))^(1/2))^(1/2)

    Please find the derivative. or atleast explain how so i may attempt and show prof.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    See attachment--be kijnd to your professor its not a difficult pblm but is not easy in front of group of people
    Attached Thumbnails Attached Thumbnails Real quick derivative answer and maybe explain?-chrule3.jpg  
    Last edited by Calculus26; February 18th 2010 at 09:16 AM.
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  3. #3
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    Quote Originally Posted by mib7289 View Post
    Yesterday in my calc class I possed a derivative problem to my professor who spent 40 mins on the problem... burned all class and didnt come up with an answer so I ask you if you know.

    y=sqrt(x+sqrt(x+sqrt(x)))

    written differently y=(x+(x+(x)^(1/2))^(1/2))^(1/2)

    Please find the derivative. or atleast explain how so i may attempt and show prof.
    y = [x + (x + x^{\frac{1}{2}})^{\frac{1}{2}}]^{\frac{1}{2}}

    It's just chain rule. It will get messy but it's not a hard problem

    \frac{1}{2[x + (x + x^{\frac{1}{2}})^{\frac{1}{2}}]^{\frac{1}{2}}} \cdot 1 + \frac{1}{2(x+x^\frac{1}{2})^\frac{1}{2}} \cdot 1 +\frac{1}{2x^{\frac{1}{2}}}

    Pretty sure that's it.

    Edit:
    Quote Originally Posted by Calculus26 View Post
    See attachment--
    Looks like I may have missed the 3rd term. But I don't think any of the substitution is necessary.
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Shananay you are correct-- I diiferentiated one term twice I changed the attachment to reflect this
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  5. #5
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    Quote Originally Posted by Calculus26 View Post
    Shananay you are correct-- I diiferentiated one term twice I changed the attachment to reflect this
    okay good, I kept looking at it and was confused why the answers differed
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