Question

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

f ''(x) =

Answer 1

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

Answer 2

f(x) = x^8e^x

Answer 3

Diffrentiate it and reply your answer

Answer 4

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

Answer 5

(8x^7)(e^x)+(x^8)(e^x)

Answer 6

that answer is good for f'(x).

Answer 7

how do i do f''(x)

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

thank you

Answer 15

you may need to gather like terms...

Answer 16

okaay

Answer 17

would it be 16x^7(e^x)

Answer 18

yep!

Answer 19

i got it wrong

Answer 20

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

Answer 21

(56x^6)(e^x)+(x^8)(e^x)+(16x^7)(e^x)

Answer 22

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

Answer 23

ohhh

Answer 24

have to simplify

Answer 25

i got ti thank you

Answer 26

cool.