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education/math/MATH1210 (calc 1)/Derivatives.md
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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:
$$ \dfrac{f(b) - f(a)}{b - a} $$

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education/math/MATH1220 (calc II)/Integration by Parts.md Normal file
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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:
$$$$