## v.s 3 years ago Differentiate. f(θ) = sec θ/3 + sec θ

1. Coolsector

$f(t) = \frac{ \sec(t) }{ 3 } + \sec(t)$

2. Coolsector

this is the question ?

3. Coolsector

or it's 3+sec(t) in the denominator ?

4. v.s

yeaaa

5. v.s

in the denominator

6. Coolsector

$f(t)=\frac{ \sec(t) }{ 3 + \sec(t) }$

7. Coolsector

like this ?

8. v.s

yes

9. micahwood50

In this case, use quotient rule.

10. Coolsector

grr mistake :| all over again

11. Coolsector

$f'(t) = \frac{ \sec(t)' * (3+\sec(t)) - (3+\sec(t))' * \sec(t) }{ (3+\sec(t))^2 }$

12. Coolsector

$f'(t) = \frac{ \tan(t)\sec(t) * (3+\sec(t)) - \tan(t)\sec(t) * \sec(t) }{ (3+\sec(t))^2 }$

13. Coolsector

$f'(t) = \frac{ 3\tan(t)\sec(t) }{ (3+\sec(t))^2 }$

14. Coolsector

nothing much more to do ..

15. v.s

so you expand and simplify?

16. Coolsector

the final answer ? you can expand the (3+sec(t))^2 but it's not really important ..

17. Coolsector

i used the quotient rule in order to find the derivative as you can see the procedure

18. v.s

okaay thank you :)

19. Coolsector

yw

20. v.s