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ChrisV Group Title

Find the derivative of the function. y=x/sqrt(x^2+1)

  • 2 years ago
  • 2 years ago

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  1. nanda082 Group Title
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    use uv rule

    • 2 years ago
  2. ChrisV Group Title
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    \[y=x/\sqrt{x ^{2}+1}\]

    • 2 years ago
  3. ChrisV Group Title
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    well I understand part of it

    • 2 years ago
  4. ChrisV Group Title
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    use quotient rule

    • 2 years ago
  5. badreferences Group Title
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    U-substitution, yo. Or whatever they call it nowadays.

    • 2 years ago
  6. ChrisV Group Title
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    then gemeraal power rule

    • 2 years ago
  7. ChrisV Group Title
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    general

    • 2 years ago
  8. badreferences Group Title
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    Oh, wait, derivative, not integral. XD

    • 2 years ago
  9. ChrisV Group Title
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    i get to this answer

    • 2 years ago
  10. cuddlepony Group Title
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    y=x/sqrt(x^2+1) Use Quenient and Chain rule

    • 2 years ago
  11. badreferences Group Title
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    Alright, product rule of x*(x^2+1)^(-1/2), (x^2+1)^(-1/2)-(1/2)x(2x)(x^2+1)^(-3/2) Yeah.

    • 2 years ago
  12. ChrisV Group Title
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    \[y'=(x ^{2}+1)^{1/2} - x ^{2}(x ^{2}+1)^{-1/2}/x ^{2}+1\]

    • 2 years ago
  13. ChrisV Group Title
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    thqats the derivative now i have to figure out how to simplify it

    • 2 years ago
  14. cuddlepony Group Title
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    is the answer

    • 2 years ago
  15. cuddlepony Group Title
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    oh crud made a mistake (sqrt(x^2+1)) - x(2x/2sqrt((x^(2)+1)))/(sqrt(x^2+1))^(2)

    • 2 years ago
  16. cuddlepony Group Title
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    that is the answer

    • 2 years ago
  17. ChrisV Group Title
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    because the final answer in the back of the book is \[1/\sqrt{(x ^{2}+1)^{3}}\]

    • 2 years ago
  18. ChrisV Group Title
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    thats the answer the book gives me

    • 2 years ago
  19. ChrisV Group Title
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    i know my first answer is correct but not simplified

    • 2 years ago
  20. cuddlepony Group Title
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    simplify

    • 2 years ago
  21. ChrisV Group Title
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    if i understood how to simplify it I wouldnt be here

    • 2 years ago
  22. ChrisV Group Title
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    lol

    • 2 years ago
  23. cuddlepony Group Title
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    fair enough :) i will help or try to my battery is about to die

    • 2 years ago
  24. cuddlepony Group Title
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    ( (sqrt(x^2+1)) - x(2x/2sqrt((x^(2)+1))) )/(sqrt(x^2+1))^(2) = ( (sqrt(x^2+1)) - (x/sqrt(x^(2)+1)) )/ (sqrt(x^2+1))^(2) = (sqrt(x^2+1)) / (sqrt(x^2+1))^(2) - ( (x/sqrt(x^(2)+1)) / (sqrt(x^2+1))^(2) ) = 1 / (sqrt(x^2+1))^(2) - ( (x/sqrt(x^(2)+1)) / (sqrt(x^2+1))^(2) )

    • 2 years ago
  25. badreferences Group Title
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    Truly, simplification and algebraic manipulation are the difficult parts of calculus; not the class' own namesake.

    • 2 years ago
  26. Mimi_x3 Group Title
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    Lol, yes it is in the quotient rule, thats why i hate it. xD

    • 2 years ago
  27. ChrisV Group Title
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    somehow it simplifies to

    • 2 years ago
  28. cuddlepony Group Title
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    1 / (sqrt(x^2+1))^(2) - ( (x/sqrt(x^(2)+1)) / (sqrt(x^2+1))^(2) ) = 1 / (sqrt(x^2+1))^(2) - x(sqrt(x^2+1))^(2) )/sqrt(x^(2)+1) = 1 / (sqrt(x^2+1))^(2) - x(sqrt(x^2+1))/1

    • 2 years ago
  29. cuddlepony Group Title
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    1 / (sqrt(x^2+1)) - x(sqrt(x^2+1)) sorry made a mistake

    • 2 years ago
  30. ChrisV Group Title
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    \[(x ^{2}+1)^{-3/2}(x ^{2}+1)/(x^2=1)\]

    • 2 years ago
  31. ChrisV Group Title
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    /x^2+1) oops

    • 2 years ago
  32. cuddlepony Group Title
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    But yeah try multiplying both the top and the bottom by the conjugate: (x(sqrt(x^2+1))^(2) + 1) but as far as I would go to simplify this would be it it ( x(sqrt(x^2+1))^(2) - 1 )/(sqrt(x^2+1))

    • 2 years ago
  33. MarinaDL Group Title
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    for final answer power in denominator should be 3/2

    • 2 years ago
  34. ChrisV Group Title
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    \[(\sqrt{x ^{2}+1} - x^2/\sqrt{x^2+1})/(x^2+1)\]

    • 2 years ago
  35. ChrisV Group Title
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    \[(x^2+1-x^2)/\sqrt{x^2+1}/x^2+1\]

    • 2 years ago
  36. ChrisV Group Title
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    \[1/(x^2+1)(\sqrt{x^2+1})\]

    • 2 years ago
  37. ChrisV Group Title
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    would \[(x^2+1)(\sqrt{x^2+1})= \sqrt{(x^2+1)^3}\]

    • 2 years ago
  38. ChrisV Group Title
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    because the final answer should be 1/sqrt(x+1)^3

    • 2 years ago
  39. MarinaDL Group Title
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    http://www.wolframalpha.com/input/?i=y%3Dx%2Fsqrt%28x%5E2%2B1%29+find+derivative

    • 2 years ago
  40. ChrisV Group Title
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    i understand that marina same thing i have there

    • 2 years ago
  41. ChrisV Group Title
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    (x+1)^2/3 = sqrt((x+1)^2)

    • 2 years ago
  42. ChrisV Group Title
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    ^3 oops

    • 2 years ago
  43. Diyadiya Group Title
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    you're right y\[(x^2+1) \sqrt{x^2+1}= (x^2+1)(x^2+1)^{1/2}= (x^2+1)^{3/2}\]

    • 2 years ago
  44. ChrisV Group Title
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    i do believe \[(x^2+1)(\sqrt{x^2+1}) = \sqrt{(x^2+1)^3}\]

    • 2 years ago
  45. ChrisV Group Title
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    ok :) then the way i did that is right

    • 2 years ago
  46. Diyadiya Group Title
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    Right!

    • 2 years ago
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