Two form of derivative $ f'(x) = \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$ Why I can write formula derivative $$ f'(x) = \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$$ in this form: $$ f'(x)=\frac{f(x+h)-f(h)}{h}+O(h)$$
I know, that it's easy but unfortunately I forgot.

Let $f(x)=|x|^{3/2}$. Then $f'(0)=0$. But $\dfrac{|h|^{3/2}-0}{h}$ is not $O(h)$.  
