Question

find the intervals on which f is increasing or decreasing f(x)=cos^2x-2sinx

Answer 1

You want to find where the derivative is positive or negative...

Answer 2

the problem here is finding the derivative

Answer 3

Using the chain rule, the derivative of cos^2 x is 2 * cos x * (-sin x) = -2 cos x sin x.

The derivative of -2 sin x is -2 cos x.

So the derivative of f(x) is -2 cos x sin x - 2 cos x = -2 cos x * (1 + sin x).

Now you want to know when that is negative or positive. (1 + sin x) is always non-negative. So it will only be non-positive if -2 cos x is non-positive, which is easy to figure out.