Left derivative: f (0-) = lim (h->; 0-)[f(h+0)-f(0)]/h = lim(h-& gt； 0-)(h-0)/h = 1；

Right derivative: f (0+) = lim (h->; 0+)[f(h+0)-f(0)]/h = lim(h-& gt； 0+)[ln( 1+h)-0]/h = lim(h-& gt； 0+) 1/( 1+h)= 1。

So there is f'(0)= 1.