Differentiation and Integration

What is Differentiation?

Differentiation is a process of finding instantaneous change in function with respect to other quantity. It is given by d/dx{f(x)} = f'(x)

What is Integration?

Integration refers to the process of adding small and continuous data of a function over a given range of limits. It is given by ∫f(x)dx = F(x) + C

What is the basic difference between Differentiation and Integration?

The basic difference between Differentiation and Integration is that Differentiation divides the function and reduces it on a particular point in the domain while Integration sums up all the continuous data of the function over a given range of limits in the domain.

What is the Differentiation of log x?

The differentiation of log x is given by d/dx(log x) which is equal to 1/x

What is Differentiation and Integration of ex?

The differentiation of ex is ex and the integration of ex is ex + C.



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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What is Differentiation?

Differentiation is a method to find the instantaneous rate of change of a function or curve with respect to other quantities. Mathematically, the Slope of the tangent at a point on the curve is called the Derivative of the Curve or Function and differentiation is a method to find that derivative. In differentiation, we compute the rate at which a dependent variable ‘y‘ changes with respect to the change in the independent variable ‘x’. This rate of change is called the derivative of ‘y’ with respect to ‘x’, where y is a function of x given as y = f(x)....

Differentiation Formulas

The derivative of standard functions can be found by the formulas. We will learn the Differentiation formulas of the following functions:...

Differentiation by Parts

In this we will learn the formulas for differentiation when two functions are in product or quotient form:...

What is Integration?

Integration is a method to find the average rate of change of a function. As the name suggests, Integrate means adding all the functions’ points. Integration is actually anti-derivative of differentiating function. Differentiation and Integration are inverses of each other. We can integrate the function in two ways one is indefinite and the other is definite. In Indefinite Integration, we get a constant C with our expression but in Definite we are able to find the value of that constant C, by restricting its range or limit. The Integration of a function f(x) is given as...

Integration Formulas

To integrate various types of functions we have different formulas for different types of functions. We will learn Integration Formulas for the following functions:...

Integration By Parts

In integration by parts, we will learn the formulas for Integration when two functions are in product or quotient form:...

Area Under the Curve

Area Under the Curve refers to the region enclosed by the graph of a function and coordinate axes or the intersection region of two graphs. Here, we will not have a regular shape hence we can’t use regular formulas. To calculate the area in such a case we will use the concept of Integration. We will take an elemental area dx under the curve and Integrate it over the defined range x = a to x = b....

Differentiation and Integration Formulas

The formulas for Differentiation and Integration of some frequently used functions are tabulated below:...

Properties of Differentiation and Integration

The Properties of Differentiation and Integration are listed below:...

Difference between Differentiation and Integration

The difference between Differentiation and Integration are as follows:...

Solved Examples of Differentiation and Integration Formula

Example 1: Differentiate [Tex]\bold{y= \frac{1}{3x+1}}   [/Tex] with respect to x....

FAQs on Differentiation and Integration

What is Differentiation?...

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