iop360
find the slope of the line tangent to the following curve at x=1...



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iop360
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\[y = \sin \left[ x  \tan(\frac{ \Pi }{ 4 }x ^{66}) \right] + x ^{\frac{ 1 }{ 1+66\Pi }}\]

iop360
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slope of the line TANGENT to this curve at x =1

iop360
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answer: 99Pi

iop360
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\[y' = \cos \left[ x  \tan(\frac{ \Pi }{ 4 }x ^{66})\right](1  \sec ^{2}(\frac{ \Pi }{ 4 }x ^{66}))(2\sec(\frac{ \Pi }{ 4 }x ^{66}))(\frac{ 33\Pi }{ 2 }x ^{65}) + \frac{ 1 }{1+66\Pi }x ^{\frac{ 1 }{ 1+66\Pi }1}\]

iop360
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is what i get for the derivative

iop360
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damn even this is too long

iop360
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could you guys verify the derivative expression

iop360
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if youre working on this

Edutopia
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what kind of sadistic math teacher gave you this problem....

helder_edwin
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what is the power of x to the right??

Edutopia
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you have to use chain rule then substitute x=1.

Edutopia
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your y(prime) is correct up to 2sec...

Edutopia
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\[66pix^{65}/4\]

Edutopia
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the above should be in place of your 2sec value... then add the derivative of that last value and substitute x=1