For the given position vectors $\mathbf{r}(t)$,
compute the (tangent) velocity vector $\mathbf{r}'(t)$ for the given value of $t$ .

A) $\displaystyle \textrm{Let } \mathbf{r}(t)= (\cos 5t,\, \sin 5t )$.
Then $\mathbf{r}'(\frac{\pi}{4})$= ( , )?

B) $\displaystyle \textrm{Let } {\mathbf{r}}(t)= (t^2,t^3)$.
Then ${\mathbf{r}}'(4)$= ( , )?

C) $\displaystyle \textrm{Let } \mathbf{r}(t)= e^{5t}\mathbf{i}+ e^{-4t}\mathbf{j}+ t\mathbf{k}$.
Then $\mathbf{r}'(1)$= $\mathbf{i}+$ $\mathbf{j}+$ $\mathbf{k}$ ?

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