f(x)= x- [x] ,x is a real number,then find f' (1/2).

Question

f(x)= x- [x] ,x is a real number,then find f' (1/2).

Answer 1

f'(1/2)=Lim_h→0(f(1/2+h)-f(1/2))/h=

=Lim_h→0(1/2+h-[1/2+h]-(1/2-[1/2])/h=

=Lim_h→0(1/2+h-1/2)/h=

=Lim_h→0h/h=1.