Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises - Page 815: 16

$\textbf{r}'(0) = \langle 1, 3, 5\rangle$

$\textbf{r}(t) = \langle f(t), g(t), h(t)\rangle$ $\textbf{r}'(t) = \langle f'(t), g'(t), h'(t)\rangle$ $\textbf{r}(t) = \langle e^t, e^{3t}, e^{5t}\rangle$ $\textbf{r}'(t) = \langle e^t, 3e^{3t}, 5e^{5t}\rangle$ $\textbf{r}'(0) = \langle e^{(0)}, 3e^{3(0)}, 5e^{5(0)}\rangle = \langle 1, 3, 5\rangle$