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find the slope of the line tangent to the following curve at x=1...

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

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Other answers:

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