## anonymous 5 years ago how to solve dy/dx: cos*2X

1. anonymous

derivative of cos (chain 2x)

2. anonymous

sin2x*2

3. anonymous

Are you sure, Starica is getting ready to correct you

4. anonymous

awww i thought we r to find dy/dx :S

5. anonymous

you just derive the outside and inside ^_^ outside = cos inside 2x so dy/dx of cos = -sin and dy/dx of 2x = 2 soooo, dy/dx cos(2x) = -2sin(2x)

6. anonymous

o_o... but wasn't she right?

7. anonymous

no i missed the negative sign

8. anonymous

isn't it finding the derivative of cos(2x)?

9. anonymous

lol, it's alright :)

10. anonymous

i guessed it so

11. anonymous

you were close =P

12. anonymous

thanks:p

13. anonymous

np ^_^, do you get it now sandip?

14. anonymous

no its finding the derivative of cos^2x

15. anonymous

OH! so the question is: $\frac{dy}{dx} \cos^2(x)$?

16. anonymous

ya

17. anonymous

alright so we have 2 steps, first outside then inside, our outside here is the power and the inside is cos(x) so dy/dx = - 2cos(x) sin(x) ^_^

18. anonymous

but star ...dont u think it must b y= cos^2x n find dy/dx??

19. anonymous

yeah lol

20. anonymous

wasn't I right? o_o

21. anonymous

... Go by the definition of the chain rule. $Let\ (cos\ x)^2 = f(g(x))$ What is our f(x), what is our g(x)?

22. anonymous

she/he doesn't get the chain rule >_< lol

23. anonymous

in a much simpler way do it this way: cos(x) . cos(x) u'v + uv' ^_^ and solve

24. anonymous

I hope this way helps though :)

25. anonymous

alright gtg, later ^_^

26. anonymous

he-she isn't going to be able to do any of the rest of their homework if they don't understand the chain rule. This is a good opportunity to learn the chain rule since you need it to solve this problem.

27. anonymous

What can I say. Star likes manual labor.

28. anonymous

lol, I'm just trying to get it clear for him/her ^_^?