anonymous
  • anonymous
Find f '(x) and f ''(x). f(x) = x^8ex f '(x) = f ''(x) =
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[f(x)=x^8e^x\]?
anonymous
  • anonymous
f(x) = x^8e^x
goformit100
  • goformit100
Diffrentiate it and reply your answer

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anonymous
  • anonymous
product rule for this one use \[(fg)'=f'g+g'f\] with \(f(x)=x^8,f'(x)=8x^7,g(x)=e^x,g'(x)=e^x\)
anonymous
  • anonymous
(8x^7)(e^x)+(x^8)(e^x)
cruffo
  • cruffo
that answer is good for f'(x).
anonymous
  • anonymous
how do i do f''(x)
cruffo
  • cruffo
\(\large f'(x) = 8x^7e^x + x^8e^x\) just take the derivative of each term in the sum above using product rule
anonymous
  • anonymous
f''(x) = (56x^6)(e^x)+(8x^7)(e^x)
cruffo
  • cruffo
that is the derivative of the first term, but not f''(x) yet.
anonymous
  • anonymous
f''(x) = ((56x^6)(e^x)+(8x^7)(e^x))+((8x^7)(e^x)+(8x^7)(e^x))
cruffo
  • cruffo
good except for the last term in you answer \[f''(x) = 56^6e^x + 8x^7e^x + 8x^7e^x + x^8e^x\]
cruffo
  • cruffo
sorry, missed an x :) \[f''(x) = 56x^6e^x + 8x^7e^x + 8x^7e^x + x^8e^x\]
anonymous
  • anonymous
thank you
cruffo
  • cruffo
you may need to gather like terms...
anonymous
  • anonymous
okaay
anonymous
  • anonymous
would it be 16x^7(e^x)
cruffo
  • cruffo
yep!
anonymous
  • anonymous
i got it wrong
cruffo
  • cruffo
maybe you also need to factor it??? \[f''(x) = 56x^6e^x + 16x^7e^x + x^8e^x\] \[GCF = x^6e^x\]
anonymous
  • anonymous
(56x^6)(e^x)+(x^8)(e^x)+(16x^7)(e^x)
cruffo
  • cruffo
maybe you also need to factor it??? \[f''(x) = 56x^6e^x + 16x^7e^x + x^8e^x\] \[GCF = x^6e^x\]
anonymous
  • anonymous
ohhh
anonymous
  • anonymous
have to simplify
anonymous
  • anonymous
i got ti thank you
cruffo
  • cruffo
cool.

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