Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises - Page 815: 20

$\textbf{r}'(ln(3)) = \langle 6, \frac{-2}{9}, 72\rangle$

$\textbf{r}(t) = \langle f(t), g(t), h(t)\rangle$ $\textbf{r}'(t) = \langle f'(t), g'(t), h'(t)\rangle$ $\textbf{r}(t) = \langle 2e^t, e^{-2t}, 4t^{2t}\rangle$ $\textbf{r}'(t) = \langle 2e^t, -2e^{-2t}, 8t^{2t}\rangle$ $\textbf{r}'(ln(3)) = \langle 2e^{ln(3)}, -2e^{-2ln(3)}, 8t^{2ln(3)}\rangle = \langle 6, \frac{-2}{9}, 72\rangle$