Introduction
Precalculus
Getting Started
Calculus 1
1. Limits
3. Derivatives
5. Applications of Derivatives
6. 1. Increasing and Decreasing Function
  2. Minimum and Maximum Values
7. Integrals
8. 1. Indefinite Integrals
  2. Computing Indefinite Integrals
  3. Substitution Rule for Indefinite Integrals
  4. Area Problem
Calculus 2
1. Integration Techniques
2. 1. Integration by Parts
  2. Integrals Involving Trig Functions
  3. Trig Substitutions
  4. Partial Fractions
  5. Integrals Involving Roots
  6. Integrals Involving Quadratics
3. Parametric Equations and Polar Coordinates
4. 1. Differentiation Formulas
  2. Product and Quotient Rule
  3. Chain Rule
  4. Implicit Differentiation
  5. Higher Order Derivatives
  6. Logarithmic Differentiation
5. Series and Sequences
6. 1. Indefinite Integrals
  2. Computing Indefinite Integrals
  3. Substitution Rule for Indefinite Integrals
  4. Area Problem
7. Vectors
8. 3-Dimensional Space
Calculus 3
1. LimitThree Dimensional Coordinate Systems
2. 1. Equations of Lines
  2. Equations of Planes
  3. Quadratic Surfaces
  4. Functions of Multiple Variables
3. Partial Derivatives
4. 1. Higher Order Partial Derivatives
  2. Differentials
  3. Chain Rule
  4. DirectioChain Rulenal Derivatives
  5. Gradient
5. Multiple Integrals
6. 1. Iterated Integrals in Cylindrical Coordinates
  2. Double Integrals
  3. Double Integrals in Polar Coordinates
  4. Triple Integrals in Spherical Coordinates
  5. Change of Variables
  6. Surface Area
7. Line Integrals
8. 1. Line Integrals With Respect to Arc Length
  2. Double Integrals in Polar Coordinates
  3. Line Integrals With Respect to x and y
  4. Line Integrals of Vector Fields
  5. Fundamental Theorem of Line Integrals
  6. Conservative Vector Fields
  7. Potential Functions
  8. Green's Theorem
9. Surface Integrals
10. 1. Parametric Surfaces
  2. Surface Integrals
  3. Surface Integrals of Vector Fields
  4. Stokes' Theorem
  5. Divergence Theorem
Cheatsheet

Derivatives

What is Derivatives?

In calculus, a derivative is a mathematical operation that describes how a function changes as its input variables (such as x in the equation f(x)) are varied. The derivative of a function at a given point is a measure of the slope of the function at that point, and it can be calculated using the following formula:

$$ \frac{dy}{dx} = \lim_{\Delta x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x} $$

This formula shows that the derivative of a function is the slope of the tangent line to the function at a given point. In other words, it represents the rate at which the output of the function (y) changes as the input (x) changes.

Example of Derivatives

$$\frac{d}{dx} (\log_5 (x))^{x/2}$$

Calculus Guide

Derivatives

What is Derivatives?

Example of Derivatives

Resources