- If $\boldsymbol{r}(t)$ represents position with time, then the graph of endpoints of $\boldsymbol{r}(t)$ represents the Cartesian path.
- Domain of $\boldsymbol{r}(t)$ is the range of $x(t)$
- Range of $\boldsymbol{r}(t)$ is the range of $y(t)$
+
+## Vector calculus
+
+### Derivative
+
+Let $\boldsymbol{r}(t)=x(t)\boldsymbol{i} + y(t)\boldsymmbol(j)$. If both $x(t)$ and $y(t)$ are differentiable, then:
+
+$$\boldsymbol{r}(t)=x(t)\boldsymbol{i}+y(t)\boldsymbol{j}$$