Differentiating Inverse Trigonometric Functions

Inverse trigonometric functions are crucial tools in calculus for handling integrals, derivatives, and equations involving trigonometric expressions. This guide explains how to differentiate these functions step-by-step, with formulas and examples.

1. Overview of Inverse Trigonometric Functions

Inverse trigonometric functions reverse the usual trigonometric functions, returning angles from known ratios. The key inverse trig functions include:

2. Derivatives of Inverse Trigonometric Functions

The standard derivatives of these functions are derived using implicit differentiation and are as follows:

3. Using the Chain Rule

When the argument of an inverse trig function is not simply xxx, apply the chain rule:

4. Examples

5. Key Takeaways