anonymous
  • anonymous
find the slope of the line tangent to the following curve at x=1...
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[y = \sin \left[ x - \tan(\frac{ \Pi }{ 4 }x ^{66}) \right] + x ^{\frac{ 1 }{ 1+66\Pi }}\]
anonymous
  • anonymous
slope of the line TANGENT to this curve at x =1
anonymous
  • anonymous
answer: -99Pi

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anonymous
  • anonymous
\[y' = \cos \left[ x - \tan(\frac{ \Pi }{ 4 }x ^{66})\right](1 - \sec ^{2}(\frac{ \Pi }{ 4 }x ^{66}))(2\sec(\frac{ \Pi }{ 4 }x ^{66}))(\frac{ 33\Pi }{ 2 }x ^{65}) + \frac{ 1 }{1+66\Pi }x ^{\frac{ 1 }{ 1+66\Pi }-1}\]
anonymous
  • anonymous
is what i get for the derivative
anonymous
  • anonymous
damn even this is too long
anonymous
  • anonymous
could you guys verify the derivative expression
anonymous
  • anonymous
if youre working on this
anonymous
  • anonymous
what kind of sadistic math teacher gave you this problem....
helder_edwin
  • helder_edwin
what is the power of x to the right??
anonymous
  • anonymous
you have to use chain rule then substitute x=1.
anonymous
  • anonymous
your y(prime) is correct up to 2sec...
anonymous
  • anonymous
\[66pix^{65}/4\]
anonymous
  • anonymous
the above should be in place of your 2sec value... then add the derivative of that last value and substitute x=1

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