Derivative Calculation Formula (Basic Differentiation Rules)

Introduction

In calculus, derivatives provide a powerful tool for analyzing the behavior of functions, particularly in determining rates of change, slopes of tangent lines, and local extrema. The derivative of a function at a given point represents the instantaneous rate of change, and mastering the basic differentiation rules is essential for solving complex problems in mathematics, physics, engineering, and economics. These rules allow for the differentiation of a wide variety of functions, including polynomials, trigonometric functions, exponential functions, and more. This article explores the fundamental differentiation rules, their formulations, and their applications in mathematical analysis.

Core Content

Power Rule

The power rule is one of the most fundamental rules in differentiation. It states that if a function is of the form $ f(x) = x^n $, where $ n $