First Principle of Differentiation
The first principle of differentiation, also known as the first principle of calculus or the difference quotient, is a fundamental concept in calculus used to find the derivative of a function at a given point. It involves taking the limit of the average rate of change of a function over an interval as the interval approaches zero.
Mathematically, the first principle of differentiation is expressed as follows:
Given a function f(x) , the derivative f'(x) at a point x = a is defined by the limit:
[Tex] f'(a) = \lim_{{h \to 0}} \frac{{f(a+h) – f(a)}}{h} [/Tex]
Fundamental of Differential Calculus
Differential calculus is a branch of calculus that studies the concept of a derivative and its applications. Derivative tells us about the rate at which a function changes at any given point. Differential Calculus is crucial to many scientific and engineering areas since it allows for the estimation of instantaneous rates of change and curve slopes. In this article, we will be discussing about Differential Calculus and its fundamentals, which every students should know.
This article helps learners in understanding of differential calculus, its concepts, and its applications. By the end of this article, readers should be able to understand the fundamentals of derivatives and use them to solve real-world issues.
Table of Content
- Key Concepts in Differential Calculus
- Limits
- Continuity
- Derivatives:
- Differentiation Notation
- Basic Rules of Differentiation
- Product Rule of Derivative
- Quotient Rule of Derivatives
- Sum Rule of Derivative
- Power Rule of Derivative
- Constant Multiple Rule of Derivative
- Chain Rule of Derivative
- Differentiation of Common Functions
- First Principle of Differentiation
- Techniques of Differentiation
- Applications of Differential Calculus
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