From 1bf9047fff21fcd00ce0af987ae04bf2dcd8f977 Mon Sep 17 00:00:00 2001
From: arc <zleyyij@users.noreply.github.com>
Date: Thu, 30 Jan 2025 09:33:44 -0700
Subject: [PATCH] vault backup: 2025-01-30 09:33:44

---
 .obsidian/plugins/obsidian-git/data.json      | 27 +++++++++++++++++++
 .../math/MATH1210 (calc 1)/Derivatives.md     | 11 +++++---
 2 files changed, 35 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 6818cb6..3ac69bf 100644
--- a/education/math/MATH1210 (calc 1)/Derivatives.md	
+++ b/education/math/MATH1210 (calc 1)/Derivatives.md	
@@ -34,9 +34,10 @@ Given the equation $y = f(x)$, the following are all notations used to represent
 - Where a sharp turn takes place
 - If the slope of the tangent line is vertical
 
-# Higher Order Differentials
-- Take the differential of a differential
+# Higher Order Derivatives
+- Take the derivative of a derivative
 
+# Exponential Derivative Formula
 Using the definition of a derivative to determine the derivative of $f(x) = x^n$, where $n$ is any natural number.
 
 $$ f'(x) = \lim_{h \to 0} \dfrac{(x + h)^n - x^n}{h} $$
@@ -61,4 +62,8 @@ $$ \dfrac{(x + h)^n - x^n}{h} = \lim_{h \to 0} \dfrac{(x^n + nx^{n-1}h + P_{n3}x
 $x^n$ cancels out, and then $h$ can be factored out of the binomial series. 
 
 This leaves us with:
-$$ \lim_{h \to 0} nx^{n-1} + P_{n3} x^{} $$
\ No newline at end of file
+$$ \lim_{h \to 0} nx^{n-1} + P_{n3} x^{n-2}*0 \cdots v * 0 $$
+
+The zeros leave us with:
+
+$$ f(x) = n, \space $f'(x) = nx^{n-1} $$