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KarateChopKid

  • 4 years ago

How would one differentiate the following: 2x+3/√(1-2x)

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  1. baddinlol
    • 4 years ago
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    You can use the quotient rule.

  2. baddinlol
    • 4 years ago
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    Are you familiar with that?

  3. KarateChopKid
    • 4 years ago
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    yes I am familiar with this

  4. baddinlol
    • 4 years ago
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    so u = 2x+3 u' = 2 v = √(1-2x) v' = -1/√(1-2x)

  5. baddinlol
    • 4 years ago
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    The quotient rule says dy/dx = (u'v - uv')/v^2

  6. KarateChopKid
    • 4 years ago
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    ok and from there I begin to distribute, correct?

  7. gurvinder
    • 4 years ago
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    u can do it with quotient rule

  8. baddinlol
    • 4 years ago
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    Thats it follow (u'v - uv')/v^2

  9. shana91
    • 4 years ago
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    |dw:1331119146075:dw| use this this is the division rule

  10. shana91
    • 4 years ago
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    where u and v are two fuctions

  11. KarateChopKid
    • 4 years ago
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    I think that the square root in the function os throwing me off but I think that it would disappear in the deno. right? just leaving 1-2x on the bottom?

  12. shana91
    • 4 years ago
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    exactly. you are right. square root dissapears. THat makes the sum a lot easier

  13. .Sam.
    • 4 years ago
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  14. KarateChopKid
    • 4 years ago
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    Thank you! I was working it out and ended with the same result.

  15. KarateChopKid
    • 4 years ago
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    One final question... how would you find the eq. of a line tangent to the graph f(x) = √(2x+9) at x=0 ?

  16. shana91
    • 4 years ago
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    take the first derivative of f(x) and equate all x to zero it gives the gradient of the tangent to the line at x=0

  17. .Sam.
    • 4 years ago
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    differentiate √(2x+9) then equate x=0 to the differentiated expression and get your gradient then create new equation using y-y1=m(x-x1)

  18. shana91
    • 4 years ago
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    then use y=mx+c to get the equa. of the line

  19. .Sam.
    • 4 years ago
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    to find y1 just equate x=0 to original equation, y=√(2x+9), then get your y1

  20. KarateChopKid
    • 4 years ago
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    ok I am still a little shaky on deffrentiating a radical equation, would it be 1/2x+9 ?

  21. .Sam.
    • 4 years ago
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    |dw:1331120584519:dw|

  22. shana91
    • 4 years ago
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    when u dof. the above one it'll be 1/(2x+9)^1/2

  23. shana91
    • 4 years ago
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    you have forgot the 1/2

  24. .Sam.
    • 4 years ago
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    1/2 cancelled by 2

  25. .Sam.
    • 4 years ago
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    chain rule

  26. KarateChopKid
    • 4 years ago
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    ok so using the chain rule I use a fraction to symbolize the same radical function then move the 1/2 down and subtract by 1 to get my new power...got it

  27. KarateChopKid
    • 4 years ago
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    where did the "2" on the right come from though?

  28. shana91
    • 4 years ago
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    not that 1/2 i meant the power 1/2|dw:1331120933568:dw| this should be what u getting aftr dif.

  29. .Sam.
    • 4 years ago
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    Example, |dw:1331120907510:dw|

  30. KarateChopKid
    • 4 years ago
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    Ok, so since it was in the deno. it was risen to the 2nd power and that is how is came to cancel the 1/2 right?

  31. KarateChopKid
    • 4 years ago
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    in the orig. differentation

  32. .Sam.
    • 4 years ago
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    the 2 in the numerator when differentiating, so it will cancel the 1/2

  33. .Sam.
    • 4 years ago
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    \[\huge \sqrt{x}=x ^{\frac{1}{2}}\]

  34. KarateChopKid
    • 4 years ago
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    ok I undrstand that example in omitting the radical but where did the 2 appear to make that cancel?

  35. KarateChopKid
    • 4 years ago
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    that is what is throwing me for a loop haha

  36. .Sam.
    • 4 years ago
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    the half of 2 is 1

  37. shana91
    • 4 years ago
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    wait --look at this.. this how u solve n this is whr it got cancelled|dw:1331121592002:dw|

  38. KarateChopKid
    • 4 years ago
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    nevermind it came as a result of the y' and omitting the 9

  39. KarateChopKid
    • 4 years ago
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    or making 2x+9 just 2 right?

  40. shana91
    • 4 years ago
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    I cant get u?

  41. KarateChopKid
    • 4 years ago
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    lol I can't get myself sometime haha but I think I understand that the 2 came as a result of taking the derivative of just 2x+9 resulting in just the 2 remaining...I think : /

  42. shana91
    • 4 years ago
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    ohh that one..wait this is clear the prob.|dw:1331122282837:dw| cool?

  43. KarateChopKid
    • 4 years ago
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    yea... that I what I was trying to say but I guess my wording is off. I see where the 2 came from

  44. shana91
    • 4 years ago
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    :)

  45. KarateChopKid
    • 4 years ago
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    Haha thanks. So then from there I plug in my x=0 to solve for that equation

  46. KarateChopKid
    • 4 years ago
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    and then use that solution in point-slope form

  47. shana91
    • 4 years ago
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    that is correct. :) and then use thegradient equation to find the gradient...and the eq. of the line

  48. salini
    • 4 years ago
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    hey shana as u say the 2 in the denominator cannot get cancelled...

  49. KarateChopKid
    • 4 years ago
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    which gives me 3 from the graident and 1/3 for my derivative function

  50. KarateChopKid
    • 4 years ago
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    |dw:1331123039074:dw|

  51. KarateChopKid
    • 4 years ago
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    |dw:1331123158889:dw|

  52. KarateChopKid
    • 4 years ago
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    correct?

  53. shana91
    • 4 years ago
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    correct

  54. KarateChopKid
    • 4 years ago
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    good deal! Thank you for all of you help and have an awesome day or night wherever you are!

  55. KarateChopKid
    • 4 years ago
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    |dw:1331123407516:dw|

  56. shana91
    • 4 years ago
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    hhe it'll be night :) Anytime . I love guiding others not for money but for joy. :)

  57. salini
    • 4 years ago
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    again how di u agree abt that 2 getting cancelled in the differentaition part

  58. shana91
    • 4 years ago
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    well salini, when u intergrate, the power comes to the front. ok? but when u again use the chain rule to integrate 2X u have to again multiply by 2. so they get cancelled off.

  59. salini
    • 4 years ago
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    oh yeah 2x part......

  60. salini
    • 4 years ago
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    we cant give u money here instead we give away medals!

  61. shana91
    • 4 years ago
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    I really dont do this for money.... your medals will be highly appreciated.. I just joined today n already in level 10. :) This is a good place to give away my knowledge.

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