Part 1/4:

Understanding the Derivative of Inverse Tangent Functions

In this tutorial, we delve into the nuances of derivatives, specifically focusing on the derivative of the inverse tangent function, commonly denoted as ( \text{arctan} ) or ( \tan^{-1} ). This is a continuation of our exploration into trigonometric and inverse trigonometric functions, further enhancing our mathematical toolkit.

Introduction to Inverse Functions

To understand the derivative of the inverse tangent function, we begin with the fundamental relationship of inverse functions. When we say ( y = \text{arctan}(x) ), we can also express this as ( \tan(y) = x ). This relationship is crucial as it forms the basis for deriving the derivative.