Recognising output impedance of an amplifier though inspection
I often deal with this problem, it's not trivial. 

Many times there are local feedbacks. In that case, you can avoid complicated equations. 


Find the cold resistance \$R_{out}^0\$. That is without considering the feedback. 
By visual inspection, look at how the feedback behaves. Will it increase the current drawn in response to your voltage stimulus? If yes, that means it will decrease the resistance, so the output resistance will be $$R_{out} = \frac{R_{out}^0}{1 - G_{loop}}$$


The reality is that you can't do the basic stuff all over again every time you analyze a circuit. At some point, you just have to remember a few formulas, especially since there's only a few basic configurations.