anonymous 3 years ago find the slope of the line tangent to the following curve where x = 1...

1. anonymous

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

2. anonymous

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

3. anonymous

4. anonymous

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

5. zepdrix

Oh goodness.. this one again iop? XD

6. anonymous

heh

7. zepdrix

Hmm

8. zepdrix

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

9. anonymous

yes

10. zepdrix

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

11. anonymous

i was wondering if that was confusing people

12. anonymous

i guess so

13. zepdrix

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

14. anonymous

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

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. anonymous

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

17. anonymous

lol

18. anonymous

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

19. anonymous

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

20. zepdrix

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

21. anonymous

yep

22. zepdrix

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

23. anonymous

yea

24. zepdrix

|dw:1349582282567:dw| Hmmmm...

25. anonymous

yes! i did that, now im stuck..

26. anonymous

some kind of factorization trick in there, perhaps?

27. zepdrix

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

28. anonymous

thanks anyway

29. anonymous

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

30. anonymous

online homework haha

31. anonymous

|dw:1349583464134:dw|

32. anonymous

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

33. anonymous

34. zepdrix

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

35. anonymous

yes that too

36. anonymous

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

37. anonymous

or that could make things worse

38. anonymous

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