It is only necessary to prove that f(x) is differentiable at x=0, that is, to prove that the left and right derivatives exist and are equal.

Left derivative (x tends to 0 from the left)

f '(0-)= lim(f(x)-0)/(x-0)= lim(0-0)/(x-0)= 0

Right derivative (x tends to 0 from the right)

f'(0+)=lim(f(x)-0)/(x-0)=limx^n/x=limx^(n- 1)-& gt； 0 when n >; 1

When n= 1, the right derivative of x=0 is 1.

Therefore, n>f is differentiable at 1 F(x) is x when n= 1! Differentiable at =0, but nondifferentiable at x=0.