vault backup: 2025-01-30 09:23:43

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

@@ -55,3 +55,5 @@ $$ f'(x) = \lim_{h \to 0} \dfrac{(x + h)^n - x^n}{h} $$
 - Where $n = 3$: $(x + h)^3 = 1x^3h^0 + 3x^2h^1 + 3x^1h^2 + 1x^0h^3 = 1x^3 + 3x^2h + 3xh^2 + 1h^3$
 
 Note that the coefficient follows the associated level of Pascal's Triangle (`1 3 3 1`), and $x$'s power decrements, while $h$'s power increments. The coefficients of each pair will always add up to $n$. Eg, $3 + 0$, $2 + 1$, $1 + 2$, and so on. The **second** term in the polynomial created will have a coefficient of $n$. 
+
+$$ \dfrac{(x + h)^n - x^n}{h} = \lim_{h \to 0} \dfrac{x^n + nx^{n-1}h + p_{n3}x^{n-2}h^2 + \cdots h^n}{} $$