## anonymous 5 years ago how would i find the derivative of tanx-3cos5x?

1. anonymous

do it in parts. First deal with tanx

2. anonymous

so (sinx/cosx) ?

3. anonymous

the derivative of tan is $\sec ^{2}x$

4. anonymous

sure you could also do it that way

5. anonymous

i know, but my teacher wants us using cos and sin identities right now

6. anonymous

then use the quotient rule

7. anonymous

have you learned the quotient rule?

8. anonymous

yes, but using it with these kinds of problems is still not second nature, you know?

9. anonymous

ya it will come with practice it's bottom times the derivitave of the top plus top times the derivative of the bottom all over the bottom squared.

10. anonymous

so i consider the top to be (sinx/cosx) and the bottom to be...?

11. anonymous

so cosx(cosx)-sinx(sinx)/$\cos ^{2}x$

12. anonymous

cos squared x?

13. anonymous

you will consider the top to be sinx and the bottom to be cos x

14. anonymous

so in using the quotient rule, i only deal with tanx?

15. anonymous

right that part goes on bottom and the other part goes on top so cos squared minus sin squared on top

16. anonymous

in using the quotient rule you deal with sinx/cosx

17. anonymous

In any problem where you derive a function, you derive each term seperately. That's why you use the quotient rule on the sin(x)/cos(x) only. You'll just add the result of that to the derivative of 3cos(5x). Do you know the derivative of sin(x) and cos(x)?

18. anonymous

you need to use the chain rule...See the linky... http://www.wolframalpha.com/input/?i=derivative+of+tanx-3cos5x

19. anonymous

and make sure you click on "Show the Steps"