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anonymous

  • 5 years ago

F(x) = (5x3 + 4)3 find the second derivative

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  1. anonymous
    • 5 years ago
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    step by step please

  2. anonymous
    • 5 years ago
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    I assume that the 3 is a power?

  3. anonymous
    • 5 years ago
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    well i used chain rule

  4. anonymous
    • 5 years ago
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    f'(x)=3(5x3 + 4)^2[15x^2]

  5. anonymous
    • 5 years ago
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    [45(x2)](2)(5x3 +4)1(15x3-1) + (45x2) (5x3 + 4)2

  6. anonymous
    • 5 years ago
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    \[45(5x^3+4)(x^2)\]

  7. anonymous
    • 5 years ago
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    oh again missed the exponent 2

  8. anonymous
    • 5 years ago
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    is my first step corrrect

  9. anonymous
    • 5 years ago
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    \[f'(x)=45(5x^3+4)^2(x^2)\]

  10. anonymous
    • 5 years ago
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    (45x2) (5x3 + 4)2

  11. anonymous
    • 5 years ago
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    3 is not in power?

  12. anonymous
    • 5 years ago
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    right, now how to do second derivative

  13. anonymous
    • 5 years ago
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    use product rule

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

  15. anonymous
    • 5 years ago
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    is the questions

  16. anonymous
    • 5 years ago
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    wait your derivative doesnt seem right

  17. anonymous
    • 5 years ago
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    this is not the same u posted earlier

  18. anonymous
    • 5 years ago
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    oh no its to the third power

  19. anonymous
    • 5 years ago
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    but the way you wrote the answer is different

  20. anonymous
    • 5 years ago
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    (45x^2) (5x3 + 4)2 by using chain rule

  21. anonymous
    • 5 years ago
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    then the derivative is correct:)

  22. anonymous
    • 5 years ago
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    right

  23. anonymous
    • 5 years ago
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    now use the product rule

  24. anonymous
    • 5 years ago
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    you left the 45 and x^2 separately

  25. anonymous
    • 5 years ago
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    confused me

  26. anonymous
    • 5 years ago
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    y confused?

  27. anonymous
    • 5 years ago
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    45(5x3+4)(x2)

  28. anonymous
    • 5 years ago
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    how can you separate 45 from the equation

  29. anonymous
    • 5 years ago
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    this is the second step, read the first too

  30. anonymous
    • 5 years ago
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    y seperated? it is being multiplied

  31. anonymous
    • 5 years ago
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    ok let me me work it out and see if our answers match

  32. anonymous
    • 5 years ago
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    ok take ur time

  33. anonymous
    • 5 years ago
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    (450x5 + 360 + 2250x10+3600x4 + 1440x)

  34. anonymous
    • 5 years ago
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    whats that?

  35. anonymous
    • 5 years ago
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    the expanded version of = (45x2) * 2(5x3 + 4) + 2(45x) * (5x3 + 4)2

  36. anonymous
    • 5 years ago
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    (45x2) (5x3 + 4)2

  37. anonymous
    • 5 years ago
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    became expanded version then that long ans

  38. anonymous
    • 5 years ago
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    y did u expand it?

  39. anonymous
    • 5 years ago
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    did u check the first derivative?

  40. anonymous
    • 5 years ago
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    not supposed to?

  41. anonymous
    • 5 years ago
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    but u were gonna do that

  42. anonymous
    • 5 years ago
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    hmm.. first derivative = (45x2) (5x3 + 4)2

  43. anonymous
    • 5 years ago
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    correct?

  44. anonymous
    • 5 years ago
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    it has to be

  45. anonymous
    • 5 years ago
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    used chain rule

  46. anonymous
    • 5 years ago
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    f''(x)= 90x(5x3 + 4)^2+(45x^2)2(5x^3+4)15x^2

  47. anonymous
    • 5 years ago
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    \[90x(5x^3+4)^2 + (675x^3)(5x^3+4)\]

  48. anonymous
    • 5 years ago
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    where did u get 15x2 from

  49. anonymous
    • 5 years ago
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    it was already simplified in the first derivative

  50. anonymous
    • 5 years ago
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    = [(45x2) * 2(5x3 + 4)] + [90x * (5x3 + 4)2]

  51. anonymous
    • 5 years ago
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    open that up = [(45x2) * (10x3 + 8)] + [90x * (25x9 + 40x3 + 16)]

  52. anonymous
    • 5 years ago
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    open further = = 2250x10 + 450x5 + 3600x4 + 1440x

  53. anonymous
    • 5 years ago
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    is that correct?

  54. anonymous
    • 5 years ago
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    u know how to apply chain rule?

  55. anonymous
    • 5 years ago
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    you said product rule i think thats where i made the mistake

  56. anonymous
    • 5 years ago
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    chain rule is again used in product rule

  57. anonymous
    • 5 years ago
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    ohhhh

  58. anonymous
    • 5 years ago
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    alright let me solve again and brb

  59. anonymous
    • 5 years ago
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    ok

  60. anonymous
    • 5 years ago
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    [(45x2)*2(5x3 + 4)*15x2] + [90x * 90(5x3 + 4)2]

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