Part 1/5:

Understanding the Derivative of Inverse Trigonometric Functions

When delving into calculus, particularly when studying derivatives, we encounter various rules and identities that become essential in our analyses. One area of focus is the derivatives of inverse trigonometric functions. In this article, we will specifically explore the derivative of the inverse cosine function through a structured, step-by-step approach.

Basics of Inverse Functions

To understand the derivative of the inverse cosine function, we must first clarify its definition. The inverse cosine of a variable ( x ) can be denoted as ( y = \text{cos}^{-1}(x) ). This relation means that (\cos(y) = x).