From 1544af34a468078b352c5c26cebe3af083fe85b3 Mon Sep 17 00:00:00 2001
From: arc <zleyyij@users.noreply.github.com>
Date: Thu, 30 Jan 2025 09:48:44 -0700
Subject: [PATCH] vault backup: 2025-01-30 09:48:44

---
 .obsidian/plugins/obsidian-git/data.json      | 27 +++++++++++++++++++
 .../math/MATH1210 (calc 1)/Derivatives.md     |  8 +++---
 2 files changed, 32 insertions(+), 3 deletions(-)

diff --git a/.obsidian/plugins/obsidian-git/data.json b/.obsidian/plugins/obsidian-git/data.json
index e69de29..bef4c6e 100644
--- a/.obsidian/plugins/obsidian-git/data.json
+++ b/.obsidian/plugins/obsidian-git/data.json
@@ -0,0 +1,27 @@
+{
+  "commitMessage": "vault backup: {{date}}",
+  "autoCommitMessage": "vault backup: {{date}}",
+  "commitDateFormat": "YYYY-MM-DD HH:mm:ss",
+  "autoSaveInterval": 5,
+  "autoPushInterval": 0,
+  "autoPullInterval": 5,
+  "autoPullOnBoot": true,
+  "disablePush": false,
+  "pullBeforePush": true,
+  "disablePopups": false,
+  "listChangedFilesInMessageBody": false,
+  "showStatusBar": true,
+  "updateSubmodules": false,
+  "syncMethod": "merge",
+  "customMessageOnAutoBackup": false,
+  "autoBackupAfterFileChange": false,
+  "treeStructure": false,
+  "refreshSourceControl": true,
+  "basePath": "",
+  "differentIntervalCommitAndPush": false,
+  "changedFilesInStatusBar": false,
+  "showedMobileNotice": true,
+  "refreshSourceControlTimer": 7000,
+  "showBranchStatusBar": true,
+  "setLastSaveToLastCommit": false
+}
\ No newline at end of file
diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md
index 2b12ed3..9301784 100644
--- a/education/math/MATH1210 (calc 1)/Derivatives.md	
+++ b/education/math/MATH1210 (calc 1)/Derivatives.md	
@@ -70,13 +70,15 @@ $$ f(x) = n, \space f'(x) = nx^{n-1} $$
 # Addition/Subtraction Derivative Rule
 You can add and subtract derivatives to find what the derivative of the whole derivative would be.
 
-# Factor Derivative Rule
+# Product Rule
 $$ \dfrac{d}{dx} (f(x) * g(x)) = \lim_{h \to 0} \dfrac{f(x +h) * g(x + h) - f(x)g(x)}{h} $$
 This is done by adding a value equivalent to zero to the numerator ($f(x + h)g(x) - f(x + h)g(x)$):
 $$ \dfrac{d}{dx} (f(x) * g(x)) = \lim_{h \to 0} \dfrac{f(x +h) * g(x + h) + f(x + h)g(x) - f(x+h)g(x) - f(x)g(x)}{h} $$
 
 From here you can factor out $f(x + h)$ from the first two terms, and a $g(x)$ from the next two terms.
 
-Then break into two different fractions
+Then break into two different fractions:
 
-$$\lim_{h \to 0} \dfrac{f(x + h)}{1} * * $$
\ No newline at end of file
+$$\lim_{h \to 0} \dfrac{f(x + h)}{1} * \dfrac{(g(x + h) - g(x))}{h)} + \dfrac{g(x)}{1} *\dfrac{f(x + h) - f(x)}{h} $$
+From here, you can take the limit of each fraction, therefore showing that to find the derivative of two values multiplied together, you can use the formula:
+$$ \dfrac{d}{dx}(f(x) * g(x)) = f(x) * g'(x) + f'(x)*
\ No newline at end of file