First Derivative Test problem

1. Nov 2, 2005

physics_ash82

Hi I need help using the First derivative test on this problem: f(x)= sinx divided by 1 + cos^2x . any help would be awesome.

2. Nov 2, 2005

Pseudo Statistic

What's the first derivative test?
I've heard of the second derivative test... but never the first..
Do you mean finding the minimum/maximum?

3. Nov 2, 2005

physics_ash82

yes That is what I eventually need, I can usually get the answer after I find f '(x) but the 1+ cos^2x is the part I cant figure out can you help?

4. Nov 2, 2005

Pseudo Statistic

OK,
First, this should be in the homework section, but nobody likes a slut, so just disregard this sentence. :D
f(x) = [sin x]/(1 + cos^2 x)
Differentiate using the quotient rule and the chain rule.. (for cos^2 x, which would mean (cos x)^2 which would give you the derivative 2(-sin x)(cos x) = -2sin x cos x)
Thus, you have:
f'(x) = (cos x)(1 + cos^2 x) + 2 sin^2 x cos x all over (1 + cos^2 x)^2...
Set that equal to 0 and ignore the denominator for the moment... and see what solutions you get...
Chances are one of them might just be when 1 + cos^2 x = 0 (I don't know anything about trig functions more than the basics without a calculator, so don't approach me and prove me wrong, I'm trying to help :P) and.... yeah.... I guess that'll be an asymptote...
Hope this helped some.

5. Nov 2, 2005

physics_ash82

Thank you for your help that made more since than what I got from class :P