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godorovg

3x^3+2x^2 +X+5 the derivative evalauate y' when x=3 need a little help bit rusty

  • one year ago
  • one year ago

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  1. godorovg
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    in order to the first you lower the power by one like this 3x^2+2x^1+5 that is der right?

    • one year ago
  2. UnkleRhaukus
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    you also have to divide by the original index

    • one year ago
  3. godorovg
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    you divide by 3 because of 3x^3

    • one year ago
  4. cornitodisc
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    x^n=nx^n-1

    • one year ago
  5. godorovg
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    so if I divide by 3, than that would make this x^2 instead of 3x^2 I am on the right track?

    • one year ago
  6. UnkleRhaukus
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    opps ive got mixed up

    • one year ago
  7. godorovg
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    y' 3x^2 is X^2 right?

    • one year ago
  8. UnkleRhaukus
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    i should have said times by the index \[y(x)=ax^n\qquad\Rightarrow\qquad y'(x)=anx^{n-1}\]

    • one year ago
  9. UnkleRhaukus
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    so sorry if i confused you

    • one year ago
  10. godorovg
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    so times by index makes 3x^3 Y' 6x^2 right?

    • one year ago
  11. UnkleRhaukus
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    not quite \[y(x)=3x^3\qquad y'(x)=3\times3x^2\]

    • one year ago
  12. godorovg
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    here is what I know y' when doing this you lower the power by one and something??

    • one year ago
  13. UnkleRhaukus
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    when taking the derivative multiply by the power and then lower the power

    • one year ago
  14. godorovg
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    so you are telling that power before lowering divide to y'

    • one year ago
  15. godorovg
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    like this 4x^3 so that would be 'y 4 right?

    • one year ago
  16. godorovg
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    4x

    • one year ago
  17. UnkleRhaukus
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    i ment times when i said divide originally , dont divide when taking the derivative

    • one year ago
  18. godorovg
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    can we start over plz..

    • one year ago
  19. UnkleRhaukus
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    yes ,

    • one year ago
  20. godorovg
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    y' 4x^2 would y'4x

    • one year ago
  21. UnkleRhaukus
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    \[y(x)=ax^n\qquad\Rightarrow\qquad y'(x)=n\times ax^{n-1}\] \[y(x)=4x^2\qquad\Rightarrow\qquad y'(x)=2\times 4x^{2-1}\]

    • one year ago
  22. godorovg
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    y'(x) would be 8x

    • one year ago
  23. UnkleRhaukus
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    thats right now

    • one year ago
  24. godorovg
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    okay so the power is what you are times before lowering the power?

    • one year ago
  25. UnkleRhaukus
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    that is right

    • one year ago
  26. godorovg
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    so for another example 10X^5 y'(x) 50x^4

    • one year ago
  27. UnkleRhaukus
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    you got it \(\checkmark\)

    • one year ago
  28. godorovg
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    so back to the problem now

    • one year ago
  29. UnkleRhaukus
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    \[y(x)=3x^3+2x^2 +x+5\]\[y'(x)=\]

    • one year ago
  30. godorovg
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    y'(x) 6x+4X +5

    • one year ago
  31. UnkleRhaukus
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    not quite, note that \[x=x^1\]\[5=5x^0\]

    • one year ago
  32. godorovg
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    y'(x) 9x+4+5

    • one year ago
  33. UnkleRhaukus
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    try again

    • one year ago
  34. godorovg
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    y'(x) 6x^2 +4x+5 +1

    • one year ago
  35. UnkleRhaukus
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    ok lets do this one term at a time \[(3x^3)^\prime=\]

    • one year ago
  36. godorovg
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    y'(x) 9x^2

    • one year ago
  37. UnkleRhaukus
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    right, now \[(2x^2)^\prime=\]

    • one year ago
  38. godorovg
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    y'(x) 9x^2 +2x

    • one year ago
  39. godorovg
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    y'(x) 9x^2 4+5+1

    • one year ago
  40. UnkleRhaukus
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    nope

    • one year ago
  41. godorovg
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    y'(x) 9x^2 +4X+5

    • one year ago
  42. UnkleRhaukus
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    you have the first two terms right,

    • one year ago
  43. UnkleRhaukus
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    \[f(x)=x=x^1\] \[f^\prime(x)=1\times x^{1-1}=x^0=1\]

    • one year ago
  44. godorovg
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    so y'(x) 9x^2+4x+1+5

    • one year ago
  45. UnkleRhaukus
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    the derivative of the last term \[g(x)=5=5x^0\] \[g^\prime(x)=0\times 5x^{0-1}=\]

    • one year ago
  46. godorovg
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    is 0

    • one year ago
  47. UnkleRhaukus
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    yeah the derivative of a constant is always zero

    • one year ago
  48. godorovg
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    so the end number unless it has a power drop off?

    • one year ago
  49. UnkleRhaukus
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    thats right

    • one year ago
  50. UnkleRhaukus
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    \[f(x)=x^2+5\qquad f'(x)=2x\]\[g(x)=x^2+9\qquad g'(x)=2x\]\[h(x)=x^2−71\qquad f'(x)=2x\]

    • one year ago
  51. UnkleRhaukus
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    that last one is ment to be h'

    • one year ago
  52. godorovg
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    cool love it so far because in math you can't drop anything, in calc 1 you can this is way cool..

    • one year ago
  53. godorovg
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    do you have time to do one more?

    • one year ago
  54. UnkleRhaukus
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    yeah can you get the answer to you original question now?

    • one year ago
  55. UnkleRhaukus
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    \[y(x)=3x^3+2x^2 +x+5\] \[y~'(x)=\]

    • one year ago
  56. godorovg
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    y'(x) 9x^2+4x+1

    • one year ago
  57. UnkleRhaukus
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    \[\Large\color\red\checkmark\]

    • one year ago
  58. godorovg
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    okay any other tips here?

    • one year ago
  59. UnkleRhaukus
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    \[y'(x)=\frac{\text dy(x)}{\text dx}\]

    • one year ago
  60. godorovg
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    explain a little??

    • one year ago
  61. UnkleRhaukus
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    its just a different notation, they men the same thing

    • one year ago
  62. UnkleRhaukus
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    the second has a bit more information because it explicitly say that we are to take the derivative of the function with respect to x, ie we look at the power of the x terms,

    • one year ago
  63. godorovg
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    dx(x)^1?dx

    • one year ago
  64. godorovg
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    so the power on the is 1 right?

    • one year ago
  65. godorovg
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    just to let know, I am in college not high school

    • one year ago
  66. UnkleRhaukus
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    \[y(x)=x=x^1\] \[\frac{\text dy(x)}{\text dx}=y'(x)=1\times x^{1-1}=x^0=1\]

    • one year ago
  67. UnkleRhaukus
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    im not sure what you mean by this dx(x)^1?dx

    • one year ago
  68. godorovg
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    I meant to use / not?

    • one year ago
  69. UnkleRhaukus
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    dx(x)^1/dx \[=\large \frac{\text d(x)^1}{\text dx}\]?

    • one year ago
  70. godorovg
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    yes that is what I meant to type

    • one year ago
  71. UnkleRhaukus
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    \[\frac{\text d(x)}{\text dx}=\frac{\text d(x^1)}{\text dx}=1\times x^0=1\]

    • one year ago
  72. UnkleRhaukus
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    im not sure if i am answer your question?

    • one year ago
  73. godorovg
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    okay now for the last question here how do this with y"(x) sin

    • one year ago
  74. godorovg
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    yes you have

    • one year ago
  75. UnkleRhaukus
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    should we evaluate y' in the first question when x=3 before that?

    • one year ago
  76. godorovg
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    y'(x) 9x^2+4x+1 so plug in 3 so we have y'(x) 9x^2 (3) +4x(3) +1 which is y'(x) 27x^2+ 12X +1

    • one year ago
  77. UnkleRhaukus
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    \[y(x)=3x^3+2x^2+x+5\] \[y'(x)=9x^2+4x+1\] \[y'(3)=9(3)^2+4(3)+1=9\times3\times3+4\times3+1\]

    • one year ago
  78. godorovg
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    y'(3) 81x^2+12+1

    • one year ago
  79. godorovg
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    12x

    • one year ago
  80. UnkleRhaukus
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    when you evaluate a function at a particular x value you substitute this value for x in the equation, there should be no x in left when evaluated

    • one year ago
  81. godorovg
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    sorry i mess me up by not putting the like this (3)^2

    • one year ago
  82. godorovg
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    so the answer is F'(3) 81x^2 + 12X +1

    • one year ago
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