Properties of Differentiation and Integration
The Properties of Differentiation and Integration are listed below:
- Property of Scalar Multiplication: Both Differentiation and Integration follow the rule of scalar multiplication i.e.,
d/dx{k.f(x)} = k.d/dx{f(x)} and ∫k.f(x)dx = k.∫f(x)dx
Where k is a scalar quantity.
- Property of Addition and Subtraction: If functions are in Addition and Subtraction form we need to solve Differentiation and Integration as
d/dx{f(x) ± g(x)} = d/dx{f(x)} ± d/dx{g(x)}
and
∫{f(x) ± g(x)} dx = ∫{f(x)} dx± ∫{g(x)} dx
- Differentiation and Integration are the inverse processes of each other i.e.,
d/dx{f(x)} = f'(x) and ∫f'(x) dx = f(x)
- Differentiation follows the Chain Rule i.e. if we have the function of function then the derivative of it is given as the derivative of the first function multiplied by the derivative of the second function i.e.,
d/dx{f(g(x))} = f'(x).g'(x)
- Both Differentiation and Integration can be solved for a given limit.
Differentiation and Integration Formula
Differentiation and Integration are two mathematical operations used to find change in a function or a quantity with respect to another quantity instantaneously and over a period, respectively. Differentiation is an instantaneous rate of change and it breaks down the function for that instant with respect to a particular quantity while Integration is the average rate of change that causes the summation of continuous data of a function over the given period or range. Both are inverse of each other.
In this article, we will learn about what is differentiation, what is integration, and the formulas related to Differentiation and Integration.
Table of Content
- What is Differentiation?
- How to Differentiate a Function
- Differentiation Formulas
- Derivative of Algebraic Functions
- Derivative of Exponential Functions
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Differentiation by Parts
- What is Integration?
- How to Integrate Function
- Integration Formulas
- Integration of Algebraic Functions
- Integration of Exponential Functions
- Integration of Trigonometric Functions
- Integration By Parts
- Area Under the Curve
- Differentiation and Integration Formulas
- Properties of Differentiation and Integration
- Difference between Differentiation and Integration
- Solved Examples of Differentiation and Integration Formula
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