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Cal help? find the intervals for which f is increasing or decreasing and locate all relative extrema on (0,2pi). f(x)= cos x / 1 + sin ^ 2x

Mathematics
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did you take the derivative?
Yep I got f'(x) = 2 sin(x) cos (2x) + 5 /cos (2x)-3 )^2
it is so long im not sure its right

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Other answers:

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could you help me solve that I have no idea how
use sin²(x)+cos²(x)=1-> cos²(x)=1-sin²(x), and then you will have only sin x in your equations
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raphael i'm sorry i am not following, where did the Z come from? and how does that get me to the extrema?
Z means k belong to the interger set,it's just a generical ans
x= 0 and 2 pi will be your solutions
and pi
is that my min and max solutions?
and it would be decreasing because its positive right?
min x= pi max are both x=0 and 2pi
ok got it
when sin(x)> 0 it will be decreasing x in]0,pi[ when sinx(x)<0 it will be increasing x in ]pi,2pi[
decreasing f'<0 increasing f'>0
thank you so much
you are welcome

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