## v.s 3 years ago Find f '(x) and f ''(x). f(x) = x^8ex f '(x) = f ''(x) =

1. satellite73

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

2. v.s

f(x) = x^8e^x

3. goformit100

4. satellite73

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

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

6. cruffo

that answer is good for f'(x).

7. v.s

how do i do f''(x)

8. cruffo

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

9. v.s

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

10. cruffo

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

11. v.s

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

12. cruffo

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

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

14. v.s

thank you

15. cruffo

you may need to gather like terms...

16. v.s

okaay

17. v.s

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

18. cruffo

yep!

19. v.s

i got it wrong

20. cruffo

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

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

22. cruffo

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

ohhh

24. v.s

have to simplify

25. v.s

i got ti thank you

26. cruffo

cool.