From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Sun, 19 Aug 2018 10:41:33 +0000 (+1000)
Subject: clarify calculus notes
X-Git-Tag: yr11~64
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/91c9ad36a394dd980e5a2eef6d41a09ef3fd70af

clarify calculus notes
---

diff --git a/spec/calculus.md b/spec/calculus.md
index 2b68bf5..3823f37 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -145,11 +145,11 @@ $\log_b y^{x^n} = x^n \log_b y$
 
 ### $e$ as a logarithm
 
-$$\log_e e = 1$$
+$$\operatorname{if} y=e^x, \quad \operatorname{then} x=\log_e y$$
 $$\ln x = \log_e x$$
 
 ### Differentiating logarithms
-$${d \over dx} \log_b x = {1 \over x \ln b}$$
+$${d(\log_e x)\over dx} = x^-1 = {1 \over x}$$
 
 ## Solving $e^x$