How do you differentiate sin(x)^x for all real numbers? How do you even define sin(x)^x for all real numbers?
I'm having problems doing this rigorously. Sure you can use the fact that sin(x)^x = exp(x*ln(sin(x))), but what happens when x belongs to an interval of the form [2*k*Pi-Pi,2*k*Pi]?
I'm doing first year math and our lecturer gave this function to differentiate. Is it me or is this much too hard? My graphic calculator won't even trace it let alone differentiate it!!