微积分 y=³根号下x方求导用定义,就是△y比△x的极限那堆

求导公式：[ x^(2/3) ]' = 2/3 * x^(-1/3) = 2/(3³√x)
以下t代表△x
x≠0时：
分子分母同乘：[(x+t)^(2/3) +(x+t)^(1/3)x^(1/3)+ x^(2/3)]有理化
lim(t->0) [(x+t)^(2/3) - x^(2/3)] /t
=lim(t->0) [(x+t)^2 - x^2] /{t[(x+t)^(4/3) +(x+t)^(2/3)x^(2/3)+ x^(4/3)]}
=lim(t->0) (2x+t) /[(x+t)^(4/3) +(x+t)^(2/3)x^(2/3)+ x^(4/3)]
= 2x/[ 3* x^(4/3)]
= 2/3 * x^(-1/3)
x=0:
lim(t->0) [(x+t)^(2/3) - x^(2/3)] /t
= lim(t->0) [t^(2/3)] /t
= ∞
导数不存在。

书上答案不是这个,是y=2/3³根号下x……
怎么做啊…