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anonymous

  • 5 years ago

f(x)=(3x^4)*sqrt(x) + 7/x^2*(sqrt(x)) f '(x)= ??

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  1. amistre64
    • 5 years ago
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    change the square root to an exponent

  2. amistre64
    • 5 years ago
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    3x^4 x^(1/2) + 7/(x^2 x^(1/2))

  3. amistre64
    • 5 years ago
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    3x^(9/2) + 7/(x^5/2) and work that....

  4. amistre64
    • 5 years ago
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    do you know how to do a derivative?

  5. amistre64
    • 5 years ago
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    7/(x^5/2) is its own term right? or is that (x^(5/2)) the demoniator of the whole equation?

  6. amistre64
    • 5 years ago
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    d..e...n..o..m...i..n...a..t...o....r.. lol

  7. anonymous
    • 5 years ago
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    own term

  8. anonymous
    • 5 years ago
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    haha

  9. amistre64
    • 5 years ago
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    good... :)

  10. anonymous
    • 5 years ago
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    o shoot , i thought i was replying to you but it wasnt posting

  11. anonymous
    • 5 years ago
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    yes, i know how to find derivatives

  12. anonymous
    • 5 years ago
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    i just dont know where i am going wrong

  13. amistre64
    • 5 years ago
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    step me thru what you have done and I will let you know :)

  14. anonymous
    • 5 years ago
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    (i had made them exponents as well)

  15. amistre64
    • 5 years ago
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    the first term is a breeze.... just multiply exponent and subtract "1" from it.....

  16. amistre64
    • 5 years ago
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    3x^(9/2) = 3(9/2)x^(7/2) = 27 x^(7/2) --------- 2 right?

  17. anonymous
    • 5 years ago
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    sorry got kicked out, yes that is what i have

  18. amistre64
    • 5 years ago
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    x^(7/2) = x^(6/2) x^(1/2) so if you want to clean it up some: 17 x^3 sqrt(x) ------------ for the first term... 2

  19. amistre64
    • 5 years ago
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    7 -------- how would you derive this term? (x^(5/2))

  20. anonymous
    • 5 years ago
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    ok

  21. anonymous
    • 5 years ago
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    oo i had x^3/2 not x^5/2

  22. amistre64
    • 5 years ago
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    quotient rule: I remember it like this: BT'-B'T ------ where B=bottom, and T=top B^2

  23. amistre64
    • 5 years ago
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    whose right then, me or you :)

  24. anonymous
    • 5 years ago
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    when you are combining x^2 and x^1/2 dont you add the exponents?

  25. amistre64
    • 5 years ago
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    yes... 2 + 1/2 = a mixed numeral...tern it into an improper fraction 2(2)+1 5 ------ = --- 2 2

  26. amistre64
    • 5 years ago
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    lol...a tern is a sea bird i think

  27. amistre64
    • 5 years ago
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    7 -------- lets derive this... (x^(5/2))

  28. anonymous
    • 5 years ago
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    oo duh.

  29. anonymous
    • 5 years ago
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    ok simple addition.

  30. anonymous
    • 5 years ago
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    so that would be--

  31. anonymous
    • 5 years ago
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    -35/2x^7/2

  32. anonymous
    • 5 years ago
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    may i ask you one more derivative question?

  33. amistre64
    • 5 years ago
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    5 x^(3/2) B' = -------- and T' = 0 2 -35 x^(3/2) -------------- 2 ------------------ x^5 Is what I get...

  34. amistre64
    • 5 years ago
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    sure, but lets finish this one first :)

  35. anonymous
    • 5 years ago
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    i plugged it in my school system and got the right answer :)

  36. amistre64
    • 5 years ago
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    lol ... cheater :)

  37. amistre64
    • 5 years ago
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    next question?

  38. anonymous
    • 5 years ago
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    they dont tell you what the answer is, just if you get it correct ;)

  39. anonymous
    • 5 years ago
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    if f(x) = sqrt(6x) f 'x = ?

  40. amistre64
    • 5 years ago
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    2 ways to do this; we can do a substituion and the chain rule? or simply change to exponent and solve it.. which way you want it?

  41. anonymous
    • 5 years ago
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    change to exponent

  42. amistre64
    • 5 years ago
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    ok.... sqrt(6x) = (6x)^(1/2) ....might have to still do the "extra" because of that (6x) in there...

  43. anonymous
    • 5 years ago
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    ok

  44. anonymous
    • 5 years ago
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    is this correct-- 1/(2(6x)^1/2)

  45. amistre64
    • 5 years ago
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    (1/2)(6x)^(-1/2) cleans up to: 1 -------- ;we got to multiply (use the chain rule) to use that "6x" 2sqrt(6x)

  46. amistre64
    • 5 years ago
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    that didnt turn out the way I wanted lol

  47. amistre64
    • 5 years ago
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    1 ------- times Dx(6x) 2sqrt(6x)

  48. amistre64
    • 5 years ago
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    Dx(6x) = 6

  49. anonymous
    • 5 years ago
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    i dont understand why you are taking the derivative of 6x

  50. amistre64
    • 5 years ago
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    6/2 = 3 3 ------- sqrt(6x)

  51. amistre64
    • 5 years ago
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    let me explain it like this: remember when we have f(g(x)) and want to derive it?

  52. amistre64
    • 5 years ago
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    we have to use the "chain rule" to solve it right? this problem is exactly that set up, let me show you..

  53. anonymous
    • 5 years ago
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    sorry, keep getting kicked out. i havent learned the chain rule

  54. amistre64
    • 5 years ago
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    y = sqrt(u) and u = 6x to solve dy/dx we need the chain rule: (dy/dx) = (dy/du) (du/dx) y = sqrt(u) dy/du = 1/2sqrt(u) u = 6x du/dx = 6 Do you see it?

  55. anonymous
    • 5 years ago
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    yes

  56. amistre64
    • 5 years ago
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    Do you understand it? Imagine a set of gears that are meshed together, when the first one is turned, all the others turn as well. But they depend on the funtion of the first one to determine how they are going to behave.... does that makes sense?

  57. anonymous
    • 5 years ago
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    ah, yes

  58. anonymous
    • 5 years ago
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    now i understand how you got to your final answer. thank you so much for all of your help!!!

  59. amistre64
    • 5 years ago
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    youre welcome :)

  60. anonymous
    • 5 years ago
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    definitely a 'fan' of you :)

  61. amistre64
    • 5 years ago
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    :) thanx...

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