From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Sat, 6 Jul 2019 04:12:29 +0000 (+1000)
Subject: [spec] start vector calculus
X-Git-Tag: yr12~100
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/42fe40b2a22f8f23ffd56684e4a2a31b111e6869?hp=5727605c4011fe198b16d530c572c71212945457

[spec] start vector calculus
---

diff --git a/spec/vectors.md b/spec/vectors.md
index 3a940e3..ef987fa 100644
--- a/spec/vectors.md
+++ b/spec/vectors.md
@@ -193,3 +193,11 @@ $$\boldsymbol{r}(t)=x\boldsymbol{i}+y\boldsymbol{y}$$
 - 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:
+
+$$\boldsymbol{r}(t)=x(t)\boldsymbol{i}+y(t)\boldsymbol{j}$$