## iop360 Group Title find the slope of the line tangent to the following curve where x = 1... one year ago one year ago

1. iop360 Group Title

$y = \sin[x - \tan (\frac{ \Pi }{ 4 }x^{66})] + x ^{\frac{ 1 }{ 1 + 66\Pi }}$

2. iop360 Group Title

if you cant see the exponent part at the end, its: $\frac{ 1 }{ 1+66\Pi }$

3. iop360 Group Title

4. iop360 Group Title

im currently at this step: $\frac{ -66\Pi }{ 4} + \frac{ 1 }{ 1 + 66\Pi }$

5. zepdrix Group Title

Oh goodness.. this one again iop? XD

6. iop360 Group Title

heh

7. zepdrix Group Title

Hmm

8. zepdrix Group Title

What is that symbol? Is that suppose to be pi?

9. iop360 Group Title

yes

10. zepdrix Group Title

Why don't u use lowercase? D: that's so confusing..

11. iop360 Group Title

i was wondering if that was confusing people

12. iop360 Group Title

i guess so

13. zepdrix Group Title

Hmm you sure the step you got to is correct so far? :O

14. iop360 Group Title

i got this for y prime: $y' = \cos[x - \tan(\frac{ \pi }{ 4 }x^{66})](1 - \sec^2(\frac{ \pi }{ 4 }x^{66}))(\frac{ 66\pi }{ 4 }x^{65}) + \frac{ 1 }{ 1+66\pi }x^\frac{ 1 }{ 1+66\pi }-1$

15. zepdrix Group Title

So what i tried to do is... After you get a common denominator and all that jazz.. you have something that looks like a polynomial in the numerator. And I'm not seeing it factor nicely :( at least not in any way that will cancel with the denominator. Hmmm

16. iop360 Group Title

plugged 1 in.. $y'(1) = 1(-1)(\frac{ 66\pi }{ 4 })(\frac{ 1 }{ 1+ 66\pi })$

17. iop360 Group Title

lol

18. iop360 Group Title

the factoring is the confusing part... how am i supposed to get it to -99pi

19. iop360 Group Title

unless the steps i did to get it to that point were incorrect...i dont think so

20. zepdrix Group Title

|dw:1349581968847:dw| Hmm yah your steps look good so far :o

21. iop360 Group Title

yep

22. zepdrix Group Title

Oh that last term should be addition.. my bad. The way that you have it originally wrote out.

23. iop360 Group Title

yea

24. zepdrix Group Title

|dw:1349582282567:dw| Hmmmm...

25. iop360 Group Title

yes! i did that, now im stuck..

26. iop360 Group Title

some kind of factorization trick in there, perhaps?

27. zepdrix Group Title

Mmmm I don't see one :\ Must be something else going on there. Blah I give up! XD

28. iop360 Group Title

thanks anyway

29. micahwood50 Group Title

What the **** kind of teacher give you question like that?!? Or did you make up this question on your own?

30. iop360 Group Title

online homework haha

31. iop360 Group Title

|dw:1349583464134:dw|

32. iop360 Group Title

the 4's cancel out..but then what? lol

33. iop360 Group Title

34. zepdrix Group Title

What we currently have = -51.83147906... -99pi = -311.0176727 Hmmm something isn't right, that doesn't equal -99pi

35. iop360 Group Title

yes that too

36. iop360 Group Title

i guess i could submit this answer wrong and get a similar question with different values

37. iop360 Group Title

or that could make things worse

38. micahwood50 Group Title

According to WolframAlpha, the answer is -102.68 or $1-33 \pi+\frac{1}{1+66 \pi}$ http://www.wolframalpha.com/input/?i=derivative+of++sin%28x+-+tan%28pi+%2F+4+x%5E66%29%29+%2B+x%5E%28%281%29%2F%281%2B66+pi%29%29+when+x+%3D+1