Chapter 11 - Vectors and Vector-Valued Functions - 11.6 Calculus of Vector-Valued Functions - 11.6 Exercises - Page 815: 19

$\textbf{r}'(1) = \langle 8, 9, -10\rangle$

$\textbf{r}(t) = \langle f(t), g(t), h(t)\rangle$ $\textbf{r}'(t) = \langle f'(t), g'(t), h'(t)\rangle$ $\textbf{r}(t) = \langle 2t^4,6t^{3/2},\frac{10}{t}\rangle$ $\textbf{r}'(t) = \langle 8t^3, 9t^{1/2}, \frac{-10}{t^2}\rangle$ $\textbf{r}'(1) = \langle 8(1)^3, 9(1)^{1/2}, \frac{-10}{(1)^2}\rangle = \langle 8, 9, -10\rangle$