Section 13.2: Derivatives and Integrals of Vector Functions

Just as for real-valued functions, the second derivative of a vector function \(\mathbf{r}\) is the derivative of \(\mathbf{r}'\), that is, \(\mathbf{r}'' = (\mathbf{r}')'\). For instance, the second derivative of the function in Example 3 is \[ \mathbf{r}''(t) = \langle -2\cos t, -\sin t, 0 \rangle \]