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

Differentiation Formulas

Differention Formulas

Differentiation formulas are mathematical relationships that allow us to find the derivative of a function in terms of other functions or variables. They are a useful tool in calculus for finding the derivative of functions that are not easily differentiated using the standard rules of calculus.

Here are some common differentiation formulas:

The power rule: The power rule states that the derivative of a function of the form $f(x) = x^n$ is given by:

$$\frac{d}{dx} x^n = nx^{n-1}$$

The constant multiple rule: The constant multiple rule states that the derivative of a function of the form $f(x) = c \cdot g(x)$ is given by:

$$\frac{d}{dx} (c \cdot g(x)) = c \cdot \frac{d}{dx} g(x)$$

where $c$ is a constant.

The sum rule: The sum rule states that the derivative of a function of the form $f(x) = g(x) + h(x)$ is given by:

$$\frac{d}{dx} (g(x) + h(x)) = \frac{d}{dx} g(x) + \frac{d}{dx} h(x)$$

The product rule: The product rule states that the derivative of a function of the form $f(x) = g(x) \cdot h(x)$ is given by:

$$\frac{d}{dx} (g(x) \cdot h(x)) = g(x) \cdot \frac{d}{dx} h(x) + h(x) \cdot \frac{d}{dx} g(x)$$

These are just a few examples of common differentiation formulas. There are many other formulas that are used to find the derivative of different types of functions, such as the quotient rule, the chain rule, and the implicit differentiation rule.