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Demostremos:
Por definición de derivada:
f'(x)=lim ((f(x+h)-f(x))/h) para h-> 0
Ahora bien, si f(x)=x, entonces: f(x+h)=x+h
reemplazando:
f'(x)=lim ( (x+h-x)/h ) , h->0
f'(x)=lim (h/h) , h->0
f'(x)=lim 1 , h->0
f'(x)=1
Saludos!