From 0172be7b442c388ad432a0630179789b72b7d41a Mon Sep 17 00:00:00 2001
From: Jari Kasandiredjo <jarikasan@gmail.com>
Date: Tue, 6 Feb 2024 14:48:03 +0100
Subject: [PATCH] fix typo in 'derivatoves' lecture 0 slide 81

---
 preliminaries/index.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/preliminaries/index.md b/preliminaries/index.md
index 68d937d..23869c4 100644
--- a/preliminaries/index.md
+++ b/preliminaries/index.md
@@ -1106,7 +1106,7 @@ slides: true
             <img src="00.Preliminaries.key-stage-0081anim0.svg" data-images="00.Preliminaries.key-stage-0081anim0.svg,00.Preliminaries.key-stage-0081anim1.svg,00.Preliminaries.key-stage-0081anim2.svg" class="slide-image" />
 
             <figcaption>
-            <p    >Here are some examples. The first two lines show the derivatoves we've already worked out in the Lagrange notation.<br></p><p    >The right part of the second line shows how much clearer things can become when we assume that we know which variable is dependent on which. The notation is more ambiguous, but a lot clearer.<br></p><p    >The third line shows the benefit of indicating <span class="red">the independent variable</span>. The variables a, b, c are indicated with letters in the function, but we treat them as constants: x is the only variable we change to observe the resulting change in the function above the line. The rest is treated the same way as the 3 in the exponent is. <br></p><aside    >This can get a little confusing when we combine it with the shorthand from the second line. We assume that the reader knows whether <span>a</span> is a constant, or a function of <span>a(x)</span>. If things get too ambiguous, we can always spell them out more explicitly.</aside><aside    ></aside>
+            <p    >Here are some examples. The first two lines show the derivatives we've already worked out in the Lagrange notation.<br></p><p    >The right part of the second line shows how much clearer things can become when we assume that we know which variable is dependent on which. The notation is more ambiguous, but a lot clearer.<br></p><p    >The third line shows the benefit of indicating <span class="red">the independent variable</span>. The variables a, b, c are indicated with letters in the function, but we treat them as constants: x is the only variable we change to observe the resulting change in the function above the line. The rest is treated the same way as the 3 in the exponent is. <br></p><aside    >This can get a little confusing when we combine it with the shorthand from the second line. We assume that the reader knows whether <span>a</span> is a constant, or a function of <span>a(x)</span>. If things get too ambiguous, we can always spell them out more explicitly.</aside><aside    ></aside>
             </figcaption>
             <span class="hint">click image for animation</span>
        </section>