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



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anonymous
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\[f(x)=x^8e^x\]?

v.s
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f(x) = x^8e^x

goformit100
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Diffrentiate it and reply your answer

anonymous
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product rule for this one
use
\[(fg)'=f'g+g'f\] with \(f(x)=x^8,f'(x)=8x^7,g(x)=e^x,g'(x)=e^x\)

v.s
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(8x^7)(e^x)+(x^8)(e^x)

cruffo
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that answer is good for f'(x).

v.s
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how do i do f''(x)

cruffo
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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

v.s
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f''(x) = (56x^6)(e^x)+(8x^7)(e^x)

cruffo
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that is the derivative of the first term, but not f''(x) yet.

v.s
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f''(x) = ((56x^6)(e^x)+(8x^7)(e^x))+((8x^7)(e^x)+(8x^7)(e^x))

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

cruffo
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sorry, missed an x :)
\[f''(x) = 56x^6e^x + 8x^7e^x + 8x^7e^x + x^8e^x\]

v.s
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thank you

cruffo
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you may need to gather like terms...

v.s
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okaay

v.s
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would it be 16x^7(e^x)

cruffo
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yep!

v.s
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i got it wrong

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

v.s
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(56x^6)(e^x)+(x^8)(e^x)+(16x^7)(e^x)

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

v.s
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ohhh

v.s
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have to simplify

v.s
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i got ti thank you

cruffo
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cool.