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+delim $$
+.TL
+The Derivative
+.AU
+Preston Pan
+.AI
+Pacific School of Innovation and Inquiry
+
+.NH 1
+Introduction
+.LP
+The derivative operator is one of the most important
+concepts in calculus, and one of the fundamental building blocks
+for all advanced studies regarding STEM. Therefore, it is good
+to know the basics behind the subject. I will be introducing them
+from the perspective of infinitesimal number, or the hyperreal number
+system as it is more formally known.
+
+.LP
+Imagine that you are a physicist studying rate of change. You can measure
+the position of a certain object through time, and you want to describe
+the average velocity of the object. Since you know that:
+
+.EQ
+delim $$
+v sub average = {\[*D] d(t)} over {\[*D] t}
+.EN
+
+where \[*D]d(t)