f(1)=f(1)+f(1),f(1)=0
当h趋于0时:
f(x+h)=f(x*(1+h/x))=f(x)+f(1+h/x)
lim(f(x+h)-f(x))/h=limf(1+h/x)/h
=limf(1+h/x)/h=(1/x)limf(1+h/x)-f(1))/(h/x)
=(1/x)f'(1)=1/x
即:f'(x)=1/x
f(1)=f(1)+f(1),f(1)=0
当h趋于0时:
f(x+h)=f(x*(1+h/x))=f(x)+f(1+h/x)
lim(f(x+h)-f(x))/h=limf(1+h/x)/h
=limf(1+h/x)/h=(1/x)limf(1+h/x)-f(1))/(h/x)
=(1/x)f'(1)=1/x
即:f'(x)=1/x