Basic Calculus

A short review of Calculus 1, 2, and 3, based on Calculus: Early Transcendentals (Eighth Edition).

Differentiation Rules#

Product Rule#

If $f$ and $g$ are both differentiable, then

$\frac{d}{dx}[f(x)g(x)]=f(x)g^\prime(x)+g(x)f^\prime(x)$
Quotient Rule#

If $f$ and $g$ are differentiable, then

$\frac{d}{dx}\bigg[\frac{f(x)}{g(x)}\bigg]=\frac{g(x)f^\prime(x)-f(x)g^\prime(x)}{[g(x)]^2}$
Integration#

The Substitution Rule#

If an integral has both an $x$ value and the derivative of that $x$ value, you can use u-substitution.

$\int x x^\prime dx = \int u du$Example 1: