Given r⃗(t)=⟨t2,3t⟩\vec{r}(t) = \langle t^2, 3t \rangler(t)=⟨t2,3t⟩, find the tangent vector r⃗′(t)\vec{r}'(t)r′(t).
⟨2t,3⟩\langle 2t, 3 \rangle⟨2t,3⟩
⟨t,3t⟩\langle t, 3t \rangle⟨t,3t⟩
⟨2,3⟩\langle 2, 3 \rangle⟨2,3⟩
⟨t2,3⟩\langle t^2, 3 \rangle⟨t2,3⟩