The concept of the derivative is the building block of many topics of calculus. It is important for understanding integrals, gradients, Hessians, and much more.
Đang xem: Derivative function
In this tutorial, you will discover the definition of a derivative, its notation and how you can compute the derivative based upon this definition. You will also discover why the derivative of a function is a function itself.
After completing this tutorial, you will know:
The definition of the derivative of a functionHow to compute the derivative of a function based upon the definitionWhy some functions do not have a derivative at a point
Let’s get started.
A Gentle Introduction to Function Derivatives Photo by Mehreen Saeed, some rights reserved
This tutorial is divided into three parts; they are:
The definition and notation used for derivatives of functionsHow to compute the derivative of a function using the definitionWhy some functions do not have a derivative at a point
What is the Derivative of a Function
In very simple words, the derivative of a function f(x) represents its rate of change and is denoted by either f”(x) or df/dx. Let’s first look at its definition and a pictorial illustration of the derivative.
Illustration of the Definition of a Function Derivative
In the figure, Δx represents a change in the value of x. We keep making the interval between x and (x+Δx) smaller and smaller until it is infinitesimal. Hence, we have the limit (Δ