For the given position vectors \(\mathbf{r}(t)\text{,}\)

compute the (tangent) velocity vector \(\mathbf{r}'(t)\) for the given value of \(t\) .

A) \(\displaystyle \textrm{Let } \mathbf{r}(t)= (\cos 3t,\, \sin 3t )\text{.}\)

Then \(\mathbf{r}'(\frac{\pi}{4})\)= ( , )?

B) \(\displaystyle \textrm{Let } {\mathbf{r}}(t)= (t^2,t^3)\text{.}\)

Then \({\mathbf{r}}'(4)\)= ( , )?

C) \(\displaystyle \textrm{Let } \mathbf{r}(t)= e^{3t}\mathbf{i}+ e^{-4t}\mathbf{j}+
t\mathbf{k}\text{.}\)

Then \(\mathbf{r}'(-1)\)= \(\mathbf{i}+\) \(\mathbf{j}+\) \(\mathbf{k}\) ?