Chapter 13 - Vector Functions - 13.2 Derivatives and Integrals of Vector Functions - 13.2 Exercises - Page 900: 14

\[ \vec{r}'(t)=\langle a \sin (2at), e^{bt}+bte^{bt},-c \sin (2ct) \rangle \]

\[ \vec{r}(t)=\langle\sin^2 at, te^{bt},\cos^2ct \rangle \] In order to compute \(\vec{r}\) we simply take the derivative of each component with respect to \(t\) of \(\vec{r}\). \[ \vec{r}'(t)=\langle a \sin (2at), e^{bt}+bte^{bt},-c \sin (2ct) \rangle \]