Basic  Square  Root

Nth Root

Different equivalent expressions involving nth roots and exponents.

Properties of Nth Roots and Exponents

Product Rule for Square Roots

Product Rule for Nth Roots

Quotient Rule for Square Roots

Quotient Rule for Nth Roots

Eliminating the radical in the denominator.

Rationalizing the Denominator

Distributive Property over Addition

Distributing a radical over a subtraction.

Distributive Property over Subtraction

Representing radicals using rational exponents.

Rational Exponent Representation

Multiplying numbers with fractional exponents.

Fractional Exponent Multiplication

Dividing numbers with fractional exponents.

Fractional Exponent Division

Power Rule for Radicals

Rationalizing denominators with a binomial.

Rationalizing Complex Denominators

Simplifying Radicals

Multiplying a radical expression by its conjugate.

Conjugate Multiplication

The nth root of a product of two numbers, detailed representation.

Nth Root of a Product (Detailed)

The nth root of a quotient of two numbers, detailed representation.

Nth Root of a Quotient (Detailed)

Radical Expressions Formulas

Zero Exponent Rule

Identity Rule

Product of same bases with different exponents.

Product Rule

Quotient of same bases with different exponents.

Quotient Rule

Negative Exponent Rule

Power of a Power Rule

Power of a Product Rule

Power of a Quotient Rule

Expresses a power as a fractional exponent.

Fractional Exponent Rule (x/y)

Fractional Exponent Rule (1/x)

Division of different bases raised to the same exponent.

Division Rule

Exponential Formulas

The logarithm of a number with respect to a base.

Basic Definition

Definition of Logarithm

Power Rule

Basic Logarithmic Properties

Converting logarithms to a different base.

Change of Base

Change of Base Formula

Natural Logarithm

Common Logarithm

Special Bases

Inverse relationship between exponentiation and logarithms.

Inverse of Logarithm

Logarithm as the inverse of exponentiation.

Inverse of Exponentiation

Inverse Properties

Logarithm of 1

Logarithm of 0

Logarithm of 1 and 0

Logarithm of a number raised to an exponent.

Identity with Exponents

Logarithm where the number is the base itself.

Logarithm of Base

Logarithm of Reciprocal

Logarithmic Identities

Constant Rule

Derivative of a constant times a function

Constant Multiple Rule

Derivative of the sum or difference of two functions

Sum/Difference Rule

Basic Derivative Rules

Derivative of Sine

Derivative of Cosine

Derivative of Tangent

Derivative of Cotangent

Derivative of Secant

Derivative of Cosecant

Trigonometric Functions

Derivative of Inverse Sine (arcsin)

Derivative of Inverse Cosine (arccos)

Derivative of Inverse Tangent (arctan)

Derivative of Inverse Cotangent (arccot)

Derivative of Inverse Secant (arcsec)

Derivative of Inverse Cosecant (arccsc)

Derivative of Inverse Trigonometric Functions

Derivative of e^x

Derivative of ln(x)

Derivative of a^x

Derivative of log_a(x)

Exponential and Logarithmic Functions

Derivative of the product of two functions

Derivative of the quotient of two functions

Product and Quotient Rules

Chain Rule

Second Order Derivative

Third Order Derivative

Fourth Order Derivative

Fifth Order Derivative

Sixth Order Derivative

Seventh Order Derivative

N-th Order Derivative

Higher Order Derivatives

Derivative of a function defined implicitly

Implicit Differentiation

Derivative of Hyperbolic Sine (sinh)

Derivative of Hyperbolic Cosine (cosh)

Derivative of Hyperbolic Tangent (tanh)

Derivative of Hyperbolic Cotangent (coth)

Derivative of Hyperbolic Secant (sech)

Derivative of Hyperbolic Cosecant (csch)

Derivative of Hyperbolic Functions

Using derivatives to find maximum and minimum values

Finding Extrema

Curve Sketching

Using derivatives to solve related rates problems

Applications of Derivatives

Leibniz Notation

Lagrange Notation

Notations and Symbols

Z-Score Tables

Key Trigonometric Values

Angle Sum Difference  Formulas

Trigonometric Function Transformations

Trigonometrical  Reflections

Sine Triple-Angle

Cosine Triple-Angle

Tangent Triple-Angle

Cotangent Triple-Angle

Secant Triple-Angle

Cosecant Triple-Angle

Triple-Angle Identities

Sine Double-Angle

Cosine Double-Angle

Tangent Double-Angle

Cotangent Double-Angle

Secant Double-Angle

Cosecant Double-Angle

Double-Angle Identities

Sine Half-Angle

Cosine Half-Angle

Tangent Half-Angle

Cotangent Half-Angle

Secant Half-Angle

Cosecant Half-Angle

Half-Angle Identities

Fundamental relationship between sine and cosine of the same angle.

Basic Pythagorean Identity

Relationship derived from the basic Pythagorean identity involving tangent and secant.

Tangent and Secant Pythagorean Identity

Relationship derived from the basic Pythagorean identity involving cotangent and cosecant.

Cotangent and Cosecant Pythagorean Identity

A derived identity involving sine and secant.

Derived Identity from Sine and Secant

A derived identity involving cosine and cosecant.

Derived Identity from Cosine and Cosecant

An identity expressing tangent in terms of cotangent.

Derived Identity from Tangent and Cotangent

An identity expressing cotangent in terms of tangent.

Derived Identity from Cotangent and Tangent

Pythagorean Identities

Sine Negative-Angle

Cosine Negative-Angle

Tangent Negative-Angle

Cotangent Negative-Angle

Secant Negative-Angle

Cosecant Negative-Angle

Negative-Angle Identities

Power-reduction formula for sine squared.

Sine Squared

Power-reduction formula for cosine squared.

Cosine Squared

Power-reduction formula for tangent squared.

Tangent Squared

Power-reduction formula for cotangent squared.

Cotangent Squared

Power-reduction formula for secant squared.

Secant Squared

Power-reduction formula for cosecant squared.

Cosecant Squared

Sine Cubed

Power-reduction formula for cosine cubed.

Cosine Cubed

Power-reduction formula for tangent cubed.

Tangent Cubed

Power-reduction formula for cotangent cubed.

Cotangent Cubed

Power-reduction formula for secant cubed.

Secant Cubed

Power-reduction formula for cosecant cubed.

Cosecant Cubed

Power-reduction formula for sine to the fourth power.

Sine to the Fourth Power

Power-reduction formula for cosine to the fourth power.

Two Steps Table Select