Table of Contents
Differentiation and Integration Basics
Differentiation and Integration – Introduction Formulae Rules Examples & FAQs.
Differentiation and Integration Basics
Differentiation
Differentiation is the process of finding the derivative of a function. The derivative is a measure of how a function changes as it is approached from different directions.
Integration
Integration is the process of finding the integral of a function. The integral is a measure of the area under a curve.
What is Differentiation?
Differentiation is the process of calculating the derivative of a function. The derivative is a measure of how the function changes as the input changes. It can be used to identify points of inflection, maxima, and minima.
Differentiation Rules:
There are three differentiation rules: the power rule, the product rule, and the quotient rule.
The power rule states that if
then
The product rule states that if
then
The quotient rule states that if
then
Sum or Difference Rule:
The sum or difference rule is a theorem in mathematics that states that the sum or difference of two congruent triangles is also congruent.
Product Rule:
The product rule states that the derivative of the product of two functions is the product of their derivatives.
Quotient Rule:
Derivative of the product of two functions is the product of their derivatives:
When functions are multiplied together, the derivative of the product is the product of the derivatives.
Chain Rule:
The Chain Rule states that if
f(x) = g(h(x))
then
f'(x) = g'(h(x))h'(x).
What is Integration?
Integration is the process of bringing together the various elements of a system into a cohesive whole. It involves coordinating the activities of the various parts of the system so that they work together effectively.
In business, integration is the process of aligning the various functions of a company so that they work together to achieve common goals. This may involve integrating the sales, marketing, operations, and financial functions of the company, or integrating the company with its suppliers and customers.
Integration is also a key concept in information technology. It refers to the process of combining different computer systems and software applications into a unified whole.
Real-Life Examples of Differentiation and Integration provided
Differentiation:
1. A teacher differentiates instruction for students in a classroom by using different instructional strategies and methods for different students.
2. A doctor differentiates care for patients by using different treatments for different patients.
3. A business differentiates its products by offering different products for different customers.
1. A teacher integrates instruction for students in a classroom by using different instructional strategies and methods for different students.
2. A doctor integrates care for patients by using different treatments for different patients.
3. A business integrates its products by offering different products for different customers.
Some Common Mistakes
There are many common mistakes that people make when they are first starting out in Brazilian Jiu Jitsu. Some of these mistakes are:
Not Training Enough
One of the biggest mistakes that people make when they are starting out in Brazilian Jiu Jitsu is not training enough. If you want to be good at Brazilian Jiu Jitsu, you need to be willing to put in the time and effort required to learn the techniques and master the art.
Not Training With a Gi
Another common mistake that people make when they are starting out in Brazilian Jiu Jitsu is not training with a gi. Brazilian Jiu Jitsu is a gi-based martial art, and if you want to be good at it, you need to be willing to train with a gi.
Not Training in a Safe Environment
Another mistake that people make when they are starting out in Brazilian Jiu Jitsu is not training in a safe environment. If you are not training in a safe environment, you are putting yourself at risk of getting injured.
