vault backup: 2025-08-27 11:39:05

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

@@ -1,4 +1,4 @@
-SA derivative can be used to describe the rate of change at a single point, or the *instantaneous velocity*.
+A derivative can be used to describe the rate of change at a single point, or the *instantaneous velocity*.
 
 The formula used to calculate the average rate of change looks like this:
 $$ \dfrac{f(b) - f(a)}{b - a} $$

education/math/MATH1220 (calc II)/Integration by Parts.md

@@ -0,0 +1,10 @@
+The integration by parts formula is:
+$$ \int udv = uv - \int vdu $$
+
+## Deriving the Integration by Parts Formula
+$$ \frac{d}{dx}(f(x)g(x)) = f'(x)g(x) + f(x)g'(x) $$
+1. Integrating both sides, we get:
+$$\int \frac{d}{dx} (f(x)g(x))dx = \int [f'(x)g(x) + f(x)]$$
+
+2. Therefore:
+$$$$