vault backup: 2025-01-30 09:43:44

.obsidian/plugins/obsidian-git/data.json

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education/math/MATH1210 (calc 1)/Derivatives.md

@@ -72,3 +72,11 @@ You can add and subtract derivatives to find what the derivative of the whole de
 
 # Factor Derivative 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
+
+$$\lim_{h \to 0} \dfrac{f(x + h)}{1} * * $$