Challenging Math: Where function is differentiable

Consider the function
f(x)=(1-tan(x))^cos(x)
f'(x)=(1-tan(x))^cos(x))*(-sin(x)ln(1-…

For which xE[0,2pi] is the function f(x) differentiable?

Apparently the answer is pi/2
Help would be great :)

So the function can only be differentiable where it is defined, obviously. So pi/2 is out, and 3pi/2 is out.

Then its function has to be defined at that point. I actually can't see all of the f'(x) and you already have it so I'm not going to spend a lot of time deriving it for you, but you just need to figure out where the derivative is not defined.

Remember 0^0 is not defined; that may come up somehow. Also, ln(U) is only defined when U>0