A Review of Rules of Differentiation by Differentiation from First Principles

• Author(s): Seleman Ismail
• Paper ID: 1702914
• Page: 113-125
• Published Date: 28-09-2021
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 5 Issue 3 September-2021

Abstract

In this paper, nine basic rules of differentiation are reviewed by the basic principle usually known as differentiation from first principles. It entails deriving the constant, constant multiple, sum, difference, product, quotient, reciprocal, power and chain rules, which are then used to find derivatives of selected functions. Some fundamental concepts describing the basic principle are reviewed. Particularly, the concepts limit, continuity of a function, differentiability of a function and derivative of a function are thoroughly reviewed. Analytically, the rules are obtained; and it is established that they usually take less amount of computation when the derivative of a function is calculated. Thus, the rules are easier to manipulate than the basic method. It is recommended that calculus learners should employ both methods when computing the derivative of a function to acquire full understanding of the concept differentiation. They should know exactly that the rules originated from the fundamental principle; and with them computations are easier.

Keywords

Function, Limit of a Function, Derivative of a Function, Differentiation from First Principles, Rules of Differentiation.

Citations

IRE Journals:
Seleman Ismail "A Review of Rules of Differentiation by Differentiation from First Principles" Iconic Research And Engineering Journals Volume 5 Issue 3 2021 Page 113-125

IEEE:
Seleman Ismail "A Review of Rules of Differentiation by Differentiation from First Principles" Iconic Research And Engineering Journals, 5(3)