Good question
here we go ...
[tex]f(z) = e^{\frac{z}{z-6} }\\~\\ \frac{d}{dz}(f(z))= e^{\frac{z}{z-6} }*[ \frac{z(1)-(z-6)*1}{(z-6)^2} ]=e^{\frac{z}{z-6} }*[ \frac{z-z+6}{(z-6)^2} ]\\~\\=e^{\frac{z}{z-6} }*[ \frac{6}{(z-6)^2} ][/tex]
Take it step by step, then you will get it totally understood
