1. PoofyPenguin

Here is the question:

2. PoofyPenguin

Here's what i got so far:

3. PoofyPenguin

I'm not sure if i did it right and i'm not sure where it's going?

4. PoofyPenguin

alright... i think i get it, but i don't get how or why the x becomes and e?

5. technopanda13

fancy writing

6. PoofyPenguin

@technopanda13 thank you!

7. zepdrix

Haha I was thinking the same thing :D I love that multiply lil astrix XD

8. zepdrix

Hmm your steps look really good. I don't see any mistakes. For your final answer I would rewrite the ugly exponential term back as x^(4x^4 + 2), The one in front.

9. zepdrix

Oh need an explanation on the exponentiation + log thing?

10. baldymcgee6

Yeah, it looks good to me too. But where did the e and the natural log all the sudden appear from?

11. PoofyPenguin

it was part of the hint...but i'm not sure why it works that way...

12. baldymcgee6

13. PoofyPenguin

@baldymcgee6 have a look at the attachment! it's the one labeld problem 10

14. Fazeelayaz

X^(x2+2) is same as e^(4x2+2)lnx u can use calculator to verify

15. PoofyPenguin

@Fazeelayaz alright, but how would i go about simplifying it?

16. zepdrix

|dw:1351311147700:dw|

17. baldymcgee6

ohh. sorry, I only saw you're answer :/

18. PoofyPenguin

@zepdrix i'm glad you like my astrix ;)

19. Fazeelayaz

simplyfying the answer or u want to know how they r equal

20. PoofyPenguin

@zepdrix great explanation! I understand it now! But how to simplify?

21. baldymcgee6

@PoofyPenguin the reason they give you that hint is to avoid logarithmic differentiation. But for future derivatives, I would recommend learning log diffs. This is just a loophole around it! But good work, it looks good to me.

22. zepdrix

|dw:1351311341113:dw|

23. zepdrix

Ah yes logarithmic differentiation is a good skill to have c:

24. zepdrix

What you have written for f'(x) is perfect poof, you just want to rewrite the first part without the e and natural log, undo your FIRST step that you did to it.

25. Fazeelayaz

o i understand there is another way to solve take ln on both sides of ur question the equation becomes $\ln f(x)=(4x{4}+2)lnx$

26. Fazeelayaz

now differentiate both sides by x

27. technopanda13

__━━____┓━╭━━━━━╮ ____━━____┗┓|::::::::::^━━^ ____━━____━┗|:::::::: |｡◕‿‿◕｡| ____━━____━━╰O--O----O-O-╯ here is a cat for for all you hard workers

28. zepdrix

hah :D

29. PoofyPenguin

alright! so would this be the final answer or can it be simplified more?

30. Fazeelayaz

$1/f(x)*(df(x)/dx)=...$use product rule on left side

31. PoofyPenguin

@technopanda13 cute kitty! ;P

32. zepdrix

You could get a common denominator on the inside if you wanted to, but it totally unnecessary c: Yah it looks good there.

33. Fazeelayaz

yes u have done it that's right

34. PoofyPenguin

ok! let me type it into the computer and get meh marks! :D

35. PoofyPenguin

Yayayayayayayay! I got it! Thanks so much everyone! All of you were so helpful! :D

36. zepdrix

yay team \:D/