正則関数fにたいして
Δlog(1+|f(z)|^2)=4|f'(z)|^2/(1+|f(z)|^2)
を示せ

Δlog(1+|f(z)|^2)
=Δ|f(z)|^2/(1+|f(z)|^2)-{(∂[x]|f(z)|^2)^2+(∂[y]|f(z)|^2)^2}/(1+|f(z)|^2)^2
=4|f'(z)|^2/(1+|f(z)|^2)^2

となったけど、計算間違いしてる？