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v.s

  • 2 years ago

Find f '(x) and f ''(x). f(x) = x^8ex f '(x) = f ''(x) =

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  1. satellite73
    • 2 years ago
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    \[f(x)=x^8e^x\]?

  2. v.s
    • 2 years ago
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    f(x) = x^8e^x

  3. goformit100
    • 2 years ago
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    Diffrentiate it and reply your answer

  4. satellite73
    • 2 years ago
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    product rule for this one use \[(fg)'=f'g+g'f\] with \(f(x)=x^8,f'(x)=8x^7,g(x)=e^x,g'(x)=e^x\)

  5. v.s
    • 2 years ago
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    (8x^7)(e^x)+(x^8)(e^x)

  6. cruffo
    • 2 years ago
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    that answer is good for f'(x).

  7. v.s
    • 2 years ago
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    how do i do f''(x)

  8. cruffo
    • 2 years ago
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    \(\large f'(x) = 8x^7e^x + x^8e^x\) just take the derivative of each term in the sum above using product rule

  9. v.s
    • 2 years ago
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    f''(x) = (56x^6)(e^x)+(8x^7)(e^x)

  10. cruffo
    • 2 years ago
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    that is the derivative of the first term, but not f''(x) yet.

  11. v.s
    • 2 years ago
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    f''(x) = ((56x^6)(e^x)+(8x^7)(e^x))+((8x^7)(e^x)+(8x^7)(e^x))

  12. cruffo
    • 2 years ago
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    good except for the last term in you answer \[f''(x) = 56^6e^x + 8x^7e^x + 8x^7e^x + x^8e^x\]

  13. cruffo
    • 2 years ago
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    sorry, missed an x :) \[f''(x) = 56x^6e^x + 8x^7e^x + 8x^7e^x + x^8e^x\]

  14. v.s
    • 2 years ago
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    thank you

  15. cruffo
    • 2 years ago
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    you may need to gather like terms...

  16. v.s
    • 2 years ago
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    okaay

  17. v.s
    • 2 years ago
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    would it be 16x^7(e^x)

  18. cruffo
    • 2 years ago
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    yep!

  19. v.s
    • 2 years ago
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    i got it wrong

  20. cruffo
    • 2 years ago
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    maybe you also need to factor it??? \[f''(x) = 56x^6e^x + 16x^7e^x + x^8e^x\] \[GCF = x^6e^x\]

  21. v.s
    • 2 years ago
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    (56x^6)(e^x)+(x^8)(e^x)+(16x^7)(e^x)

  22. cruffo
    • 2 years ago
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    maybe you also need to factor it??? \[f''(x) = 56x^6e^x + 16x^7e^x + x^8e^x\] \[GCF = x^6e^x\]

  23. v.s
    • 2 years ago
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    ohhh

  24. v.s
    • 2 years ago
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    have to simplify

  25. v.s
    • 2 years ago
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    i got ti thank you

  26. cruffo
    • 2 years ago
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    cool.

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