## iop360 3 years ago find the slope of the line tangent to the following curve at x=1...

1. iop360

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

2. iop360

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

3. iop360

4. iop360

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

5. iop360

is what i get for the derivative

6. iop360

damn even this is too long

7. iop360

could you guys verify the derivative expression

8. iop360

if youre working on this

9. Edutopia

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

10. helder_edwin

what is the power of x to the right??

11. Edutopia

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

12. Edutopia

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

13. Edutopia

$66pix^{65}/4$

14. Edutopia

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