What is Differentiation in Calculus?
Differentiation can be defined as a derivative of a function with respect to an independent variable. Let y = f(x) be a function of x. Then, the rate of change of “y” per unit change in “x” is given by :
f'(x)=dy / dx
Differentiation using First Principle
It states that if the function f(x) undergoes an infinitesimal small change of ‘h’ near to any point ‘x’, then the derivative of the function ( provided this limit exists ) is defined as:
f'(x)= limh → 0 [f(x+h)-f(x) ]/ h , h≠0
Differentiation Notations
If a function is denoted as y = f(x), the derivative can be indicated by the following notations.
- D(y) or D[f(x)] is called Euler’s notation.
- dy/dx is called Leibniz’s notation.
- F’(x) is called Lagrange’s notation.
The meaning of differentiation is the process of determining the derivative of a function at any point say x .
Differentiation
Differentiation in mathematics refers to the process of finding the derivative of a function, which involves determining the rate of change of a function with respect to its variables. It is a fundamental concept in calculus used to measure the function’s per unit change in the independent variable.
In this article, we will discuss the concept of Differentiation in detail including its definition, notations, various basic rules, and many many different formulas for differentiation.
Table of Content
- What is Differentiation in Calculus?
- Differentiation using First Principle
- Differentiation Rules
- Differentiation of Elementary Functions
- Differentiation Formulas
- Differentiation Techniques
- Higher Order Differentiation
- Partial Differentiation