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anonymous

  • 5 years ago

F(x) = (5x^3 + 4)^3 find second deravitive F’(x) = 3(5x^3 + 4)3-1 (15x^2) = (45x2) (5x^3 + 4)2 F”(X) = (45x^2) (5x^3 + 4)2 (45x^2)*2(5x^3 + 4)*15x2] + [90x * 90(5x^3 + 4)^2] how to open this up

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  1. amistre64
    • 5 years ago
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    my eyes are burning!!

  2. amistre64
    • 5 years ago
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    F(x) = (5x^3 + 4)^3 F'' = 3(5x^3 + 4)^2 . 15x^2

  3. watchmath
    • 5 years ago
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    \(F(x)=(5x^3+4)^3\) \(F'(x)=3(5x^3+4)^2\cdot 15x^2\) \(F''(x)=90x\cdot (5x^3+4)^2+90x^2(5x^3+4)\cdot 15x^2\)

  4. amistre64
    • 5 years ago
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    that was sposed to be F'.... F'' = 3(5x^3 + 4)^2 . 30x + 6(5x^3 + 4) 15x^2 15x^2

  5. anonymous
    • 5 years ago
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    right now what after that step

  6. amistre64
    • 5 years ago
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    that is the second derivative

  7. anonymous
    • 5 years ago
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    how do you open that up

  8. amistre64
    • 5 years ago
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    you only derive twice to find the second derivative....

  9. anonymous
    • 5 years ago
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    understood how do you open teacher wants us to open

  10. amistre64
    • 5 years ago
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    if you wanna expand it; then multiply it out..... right?

  11. amistre64
    • 5 years ago
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    90x(25x^6 + 16 + 20x^3) + 15.15.6.x^4(5x^3 +4)

  12. amistre64
    • 5 years ago
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    90x(25x^6 + 16 + 20x^3) + 1350x^4(5x^3 +4) 90(25)x^7 + (90x)16 + (90)20x^4 + 1350(5)x^7 +4(1350x^4) if i did it right

  13. anonymous
    • 5 years ago
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    your first derivative is wrong it should be 3(5x^3 + 4)3-1 (15x^2) = (45x2) (5x^3 + 4)^2

  14. anonymous
    • 5 years ago
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    3(5x^3 + 4)^2 (15x^2) = (45x^2) (5x^3 + 4)^2

  15. amistre64
    • 5 years ago
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    F' = 3(5x^3 + 4)^2 . 15x^2 this? not according to what you gave us...

  16. anonymous
    • 5 years ago
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    (5x^3 + 4)^3

  17. anonymous
    • 5 years ago
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    original right

  18. anonymous
    • 5 years ago
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    derivative of inner

  19. anonymous
    • 5 years ago
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    * chain rule

  20. amistre64
    • 5 years ago
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    F' = 45x^2 (5x-4)^2 ... we agree :)

  21. anonymous
    • 5 years ago
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    k lol

  22. anonymous
    • 5 years ago
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    now 2nd derivative

  23. amistre64
    • 5 years ago
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    to make things easier; we could just expand this right here and take the derivative afterwards

  24. anonymous
    • 5 years ago
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    smart

  25. anonymous
    • 5 years ago
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    so

  26. amistre64
    • 5 years ago
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    i have my moments lol

  27. anonymous
    • 5 years ago
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    so 25x - 40x + 16

  28. amistre64
    • 5 years ago
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    45x^2(25x^6 -40x^3 +16) right?

  29. anonymous
    • 5 years ago
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    * 45x^2

  30. anonymous
    • 5 years ago
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    how to the 6th

  31. amistre64
    • 5 years ago
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    1125x^8 -1800x^5 + 720x^2

  32. amistre64
    • 5 years ago
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    5.5.x^3.x^3 = 25x^6

  33. anonymous
    • 5 years ago
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    http://www.wolframalpha.com/input/?i=d^2%2Fdx^2%28%285x^3+%2B+4%29^3%29

  34. anonymous
    • 5 years ago
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    its to the ^2

  35. amistre64
    • 5 years ago
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    -4.-4 = +16 5.-4.2.x^3 = -40x^3

  36. amistre64
    • 5 years ago
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    just the innards; exapnding the ^2 part....

  37. amistre64
    • 5 years ago
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    then multiply in the 45x^2 after that

  38. anonymous
    • 5 years ago
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    oh you did product + chain rule

  39. amistre64
    • 5 years ago
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    1125x^8 -1800x^5 + 720x^2 is what you should get

  40. anonymous
    • 5 years ago
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    check this link http://www.wolframalpha.com/input/?i=d^2%2Fdx^2%28%285x^3+%2B+4%29^3%29 it says diff

  41. amistre64
    • 5 years ago
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    45x^2 (5x^3 -4)^2 45x^2(25x^6 -40x^3 +16) 1125x^8 -1800x^5 + 720x^2 all i did was expand it to get to here; no second derivative yet..

  42. anonymous
    • 5 years ago
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    ahhh

  43. amistre64
    • 5 years ago
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    now we can easily...or easilier... take the deriavtive of this

  44. anonymous
    • 5 years ago
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    yup

  45. amistre64
    • 5 years ago
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    1125(8)x^7 -1800(5)x^4 + 720(2)x 9000x^7 -9000x^4 + 1440x if i kept track of it all

  46. amistre64
    • 5 years ago
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    factor out the 360x now

  47. amistre64
    • 5 years ago
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    and it should match wolframs

  48. amistre64
    • 5 years ago
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    360x (25x^6 -25x^3 +4)

  49. amistre64
    • 5 years ago
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    only diff is that I got a negative from a typo in the beginning

  50. anonymous
    • 5 years ago
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    thanks man

  51. amistre64
    • 5 years ago
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    youre welcome :)

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