Question: derivatives, what am I missing?

Hello, I am new to maple 12 and am a bit lost. I am trying to do simple derivatives and it seems like maple is usually wrong when calculating even simple derivatives. I give it something like... cot(x/2) or even cot(x) and it gives me the wrong answer. Also, any quotient seems to be incorrect, a problem such as... d/dz[(z-1)/(z+1)] yields a incorrect solution. Is it just me? What am I missing? Thanks
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