## anonymous 4 years ago find the slope of the line tangent to the following curve at x=1...

1. anonymous

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

2. anonymous

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

3. anonymous

4. anonymous

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

5. anonymous

is what i get for the derivative

6. anonymous

damn even this is too long

7. anonymous

could you guys verify the derivative expression

8. anonymous

if youre working on this

9. anonymous

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

10. helder_edwin

what is the power of x to the right??

11. anonymous

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

12. anonymous

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

13. anonymous

$66pix^{65}/4$

14. anonymous

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