Consider the vector-valued function Determine whether exists

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Consider the vector-valued function

\mathbf{r}(t)=\begin{cases}\langle t^2,2t\rangle,&t\le0,\\\langle\sin t,e^t-1\rangle,&t>0.\end{cases}

Determine whether

\mathbf{r}'(0)

exists. If it exists, give its value; if not, state that it does not exist.