complex analysis - Definition of smooth curve

Definition of smooth curve: A parametric curve $\mathrm Z(t)=x(t)+i
> y(t)$ on $[a,b]$ is called smooth if

1. $\mathrm Z'(t)=x'(t)+i y'(t)$ exists and continuous on $[a,b]$.




2. $\mathrm Z'(t)$ is non zero on $(a,b)$.

But my problem is that why is the word "continuous" written? As We know that differentiability implies continuity.