anonymous
  • anonymous
find the slope of the line tangent to the following curve where x = 1...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[y = \sin[x - \tan (\frac{ \Pi }{ 4 }x^{66})] + x ^{\frac{ 1 }{ 1 + 66\Pi }}\]
anonymous
  • anonymous
if you cant see the exponent part at the end, its: \[\frac{ 1 }{ 1+66\Pi }\]
anonymous
  • anonymous
answer is -99Pi

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anonymous
  • anonymous
im currently at this step: \[\frac{ -66\Pi }{ 4} + \frac{ 1 }{ 1 + 66\Pi }\]
zepdrix
  • zepdrix
Oh goodness.. this one again iop? XD
anonymous
  • anonymous
heh
zepdrix
  • zepdrix
Hmm
zepdrix
  • zepdrix
What is that symbol? Is that suppose to be pi?
anonymous
  • anonymous
yes
zepdrix
  • zepdrix
Why don't u use lowercase? D: that's so confusing..
anonymous
  • anonymous
i was wondering if that was confusing people
anonymous
  • anonymous
i guess so
zepdrix
  • zepdrix
Hmm you sure the step you got to is correct so far? :O
anonymous
  • anonymous
i got this for y prime: \[y' = \cos[x - \tan(\frac{ \pi }{ 4 }x^{66})](1 - \sec^2(\frac{ \pi }{ 4 }x^{66}))(\frac{ 66\pi }{ 4 }x^{65}) + \frac{ 1 }{ 1+66\pi }x^\frac{ 1 }{ 1+66\pi }-1\]
zepdrix
  • 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
anonymous
  • anonymous
plugged 1 in.. \[y'(1) = 1(-1)(\frac{ 66\pi }{ 4 })(\frac{ 1 }{ 1+ 66\pi })\]
anonymous
  • anonymous
lol
anonymous
  • anonymous
the factoring is the confusing part... how am i supposed to get it to -99pi
anonymous
  • anonymous
unless the steps i did to get it to that point were incorrect...i dont think so
zepdrix
  • zepdrix
|dw:1349581968847:dw| Hmm yah your steps look good so far :o
anonymous
  • anonymous
yep
zepdrix
  • zepdrix
Oh that last term should be addition.. my bad. The way that you have it originally wrote out.
anonymous
  • anonymous
yea
zepdrix
  • zepdrix
|dw:1349582282567:dw| Hmmmm...
anonymous
  • anonymous
yes! i did that, now im stuck..
anonymous
  • anonymous
some kind of factorization trick in there, perhaps?
zepdrix
  • zepdrix
Mmmm I don't see one :\ Must be something else going on there. Blah I give up! XD
anonymous
  • anonymous
thanks anyway
anonymous
  • anonymous
What the **** kind of teacher give you question like that?!? Or did you make up this question on your own?
anonymous
  • anonymous
online homework haha
anonymous
  • anonymous
|dw:1349583464134:dw|
anonymous
  • anonymous
the 4's cancel out..but then what? lol
anonymous
  • anonymous
i guess the neg sign could be the neg sign in the answer: -99pi
zepdrix
  • zepdrix
What we currently have = -51.83147906... -99pi = -311.0176727 Hmmm something isn't right, that doesn't equal -99pi
anonymous
  • anonymous
yes that too
anonymous
  • anonymous
i guess i could submit this answer wrong and get a similar question with different values
anonymous
  • anonymous
or that could make things worse
anonymous
  • 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

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