## Calculus (3rd Edition)

$$r'(t)=\langle 1,2t,3t^2 \rangle,$$ $$r''(t)=\langle 0,2,6t \rangle .$$
Since $r(t)=\langle t,t^2,t^3 \rangle$, then the derivative $r'(t)$ is given by $$r'(t)=\langle 1,2t,3t^2 \rangle,$$ and hence the second derivative $r''(t)$ is given by $$r''(t)=\langle 0,2,6t \rangle.$$