Lecture: Differentiating Inverse Trigonometric Functions

Overview

• This lecture focuses on the differentiation of inverse trigonometric functions.
• Inverse trigonometric functions include arcsin, arccos, and arctan.

Key Concepts

Inverse Trigonometric Functions

• Arcsin: The inverse of sine, noted as ( \sin^{-1}(x) ) or ( \text{arcsin}(x) ).
• Arccos: The inverse of cosine, noted as ( \cos^{-1}(x) ) or ( \text{arccos}(x) ).
• Arctan: The inverse of tangent, noted as ( \tan^{-1}(x) ) or ( \text{arctan}(x) ).

Differentiation Rules

• Derivative of Arcsin: [ \frac{d}{dx}(\sin^{-1}(x)) = \frac{1}{\sqrt{1-x^2}} ]
• Derivative of Arccos: [ \frac{d}{dx}(\cos^{-1}(x)) = -\frac{1}{\sqrt{1-x^2}} ]
• Derivative of Arctan: [ \frac{d}{dx}(\tan^{-1}(x)) = \frac{1}{1+x^2} ]

Applications

• Understanding these derivatives is crucial for solving complex calculus problems.
• They are used in integration, particularly in solving integrals that involve inverse trigonometric functions.

Additional Resources

• More information and practice problems can be found in the recorded lessons and class materials provided on SharePoint.