From 3f65163e1778a275fb547ee91d2930652e5af85a Mon Sep 17 00:00:00 2001
From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Sat, 18 Aug 2018 16:52:23 +1000
Subject: [PATCH] logs etc

---
 spec/calculus.md | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/spec/calculus.md b/spec/calculus.md
index 4c33318..19f97b5 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -93,7 +93,7 @@ where $u$ and $v$ are functions of $x$
 
 $$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
 
-## Chain rule
+## Chain rule for $(f\circ g)$
 
 $$(f \circ g)^\prime = (f^\prime \circ g) \cdot g^\prime$$
 
@@ -130,3 +130,16 @@ If $f(x)={u(x) \over v(x)}$, then $f^\prime(x)={{v(x)u^\prime(x)-u(x)v^\prime(x)
 
 If $y={u(x) \over v(x)}$, then derivative ${dy \over dx} = {{v{du \over dx} - u{dv \over dx}} \over v^2}$
 
+## Solving $e^x$
+
+| $f(x)$ | $f^\prime(x)$ |
+| ------ | ------------- |
+| $\sin x$ | $\cos x$ |
+| $\sin ax$ | $a\cos ax$ |
+| $\cos x$ | $-\sin x$ |
+| $\cos ax$ | $-a \sin ax$ |
+| $e^x$ | $e^x$ |
+| $e^{ax}$ | $ae^{ax}$ |
+| $\log_e x$ | $1 \over x$ |
+| $\log_e {ax}$ | $1 \over x$ |
+
-- 
2.49.0