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ChrisV

  • 2 years ago

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

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  1. nanda082
    • 2 years ago
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    use uv rule

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

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

  4. ChrisV
    • 2 years ago
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    use quotient rule

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

  6. ChrisV
    • 2 years ago
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    then gemeraal power rule

  7. ChrisV
    • 2 years ago
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    general

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

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

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

  11. badreferences
    • 2 years ago
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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.

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

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

  14. cuddlepony
    • 2 years ago
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    is the answer

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

  16. cuddlepony
    • 2 years ago
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    that is the answer

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

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

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

  20. cuddlepony
    • 2 years ago
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    simplify

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

  22. ChrisV
    • 2 years ago
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    lol

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

  24. cuddlepony
    • 2 years ago
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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) )

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

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

  27. ChrisV
    • 2 years ago
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    somehow it simplifies to

  28. cuddlepony
    • 2 years ago
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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

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

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

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

  32. cuddlepony
    • 2 years ago
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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))

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

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

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

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

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

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

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

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

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

  42. ChrisV
    • 2 years ago
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    ^3 oops

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

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

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

  46. Diyadiya
    • 2 years ago
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    Right!

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