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Derivative of Inverse Trigonometric Functions

Antiderivatives

Derivatives and Antiderivatives

Derivative and Antiderivative of a Function

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Area Under Curves

Areas between curves

Average Value

Average value of a function

Basic Integration Techniques

U-Substitution

U-Substitution: Integrating Radical Functions

Not-So-Obvious U-Substitution

Concept of Limits

Finding limits from graphs

Finding limits algebraically - direct substitution

Finding limits algebraically - when direct substitution is not possible

Limit laws

Evaluating Limits of Functions

limit laws

Evaluating Limits with specific limits given

Introduction to Calculus - Limits

Continuity

Intermediate value theorem

Proving the Existence of Real Roots Using IVT

Intermediate Value Theorem

Application of Intermediate Value Theorem

Proving the Existence of a Real Root Using IVT

Discontinuities of Rational Functions (denominator=0)

Critical Points and Extrema

Critical number & maximum and minimum values

Critical Number & Maximum and Minimum Values

Optimization

Curve Analysis

Curve sketching

Derivative Concept

Estimating Derivatives from a table

Slope and equation of tangent line

Definition of derivative

Definition of Derivative

Derivative using Definition

Vertical Tangent Line of a Function

Applications to definition of derivative

Derivative Rules

Chain rule

Chain Rule

Differentiation of Trigonometric Function

Differentiate Radical Functions with Chain Rule

Differentiate: Trigonometric Functions

Chain rule: Differentiate Trigonometric Functions

Differentiation of Exponential Function

Differentiation of Exponential Functions

Differentiation: Chain Rule with Logarithmic Functions

Differentiation of Logarithmic Function

Product rule

Quotient rule

Differentiation using Quotient Rule

Differentiation using Chain Rule and Quotient Rule

Power rule

Power Rule

Application of the Power Rule

Power rule application

Applying Power Rule

Power Rule with Negative Exponents

Power rule with rational exponents

Power rule and rational exponents

Derivatives of Special Functions

Derivative of inverse trigonometric functions

Derivative of trigonometric functions

Derivative of Trigonometric Functions

Derivative of Composite Trig Functions

Derivative of exponential functions

Derivative of Exponential Functions

Differentiation of Composite Functions

Derivative of power and exponential functions

Derivative of logarithmic functions

Derivative of log with arbitrary base

Derivative of Natural Logarithm Functions

Derivative of Logarithmic Functions

Fundamental Theorem of Calculus

Fundamental theorem of calculus

Fundamental Theorem of Calculus Part II

Fundamental Theorem of Calculus Part I

Implicit Differentiation

Implicit differentiation

Limits at Infinity

Infinite limits - vertical asymptotes

Limits at infinity - horizontal asymptotes

Limit Evaluation

Limits at Infinity of Exponential Functions

Motion and Rates

Position velocity acceleration

Velocity of a Particle

Total Distance Traveled by a Particle

Comparative Analysis of Particle's Velocity and Acceleration

Riemann Sums

Riemann sum

Riemann Sum

Evaluating integrals with a Riemann sum

Evaluating integrals with a Riemann Sum

Riemann Sum with Trapezoid Approximation

Trapezoidal Approximation of Riemann Sums

Tangent Lines

Linear approximation

Use of Linear Approximations in Estimating Square Roots

Linearization of Radical Functions

Linearization of Polynomial Functions

Linearization of Rational Functions

Linearization of Exponential Functions

Linearization of Logarithmic Functions

Linear Approximation of Trigonometric Functions

Parent Assignments

Challenge Zone

Foundation Review

math

Review of inverse trig functions using a right triangle example

Deriving the derivative formula for inverse sine of x

Differentiating arc cosine of x squared using the chain rule

Differentiating 4·arccot(3x+1) using the chain rule

Differentiating arctan(e^x / x²) using quotient and chain rules

Differentiating arc secant x times arc cosecant x using the product rule

Proving the derivative of arctan(4x²) + arccot(4x²) equals zero

A clear walkthrough of the derivative of inverse trigonometric functions: the six formulas, how implicit differentiation proves the arcsin rule, and solved examples combining inverse trig with the chain rule.

Trigonometric ratios of angles in radians

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Overview

Derivative of Inverse Trigonometric Functions

What You'll Learn

The derivative of each inverse trig function comes from applying implicit differentiation to its trig definition.

The derivative of arcsin x is 1 over the square root of 1 minus x squared, and the derivative of arccos x is its negative.

The derivative of arctan x is 1 over 1 plus x squared, one of the simplest inverse trig derivative rules.

Inverse secant and inverse cosecant derivatives include an absolute value of x because their domains exclude values between negative 1 and 1.

Chain rule problems with inverse trig functions follow the same pattern as ordinary chain rule problems, just with a new set of outer function derivatives.

What You'll Practice

Finding derivatives of arcsin, arccos, and arctan with variable expressions inside

Applying chain rule to expressions like arctan(e^x) and arccot(3x+1)

Using product and quotient rules with inverse trigonometric functions

Proving derivative identities involving inverse trig functions

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

7 Video lessons

Practice exercises

Learning resources

Skills

Inverse Trigonometric Functions

Chain Rule

Implicit Differentiation

Pythagorean Identity

Product Rule

Quotient Rule

Derivatives