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Class 6 Tuition > Class 6 Tuition in Mumbai > Ashwini R.

Ashwini R. Class 6 Tuition trainer in Mumbai/>

Ashwini R.

Ace Tutor

Taloja Phase 1, Mumbai, India - 410208.

1 Student

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Referral Discount: Get ₹ 250 off when you make a payment to start classes. Get started by Booking a Demo.

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Overview

Enthusiastic about applying a passion for working with children that includes solid knowledge acquired from relevant courses.
â?¢Committed to helping children reach their full potential by fostering a supportive learning environment.
â?¢A passion about the teaching field with a great teaching aptitude
â?¢Excellent ability to reach to the target students knowledge grasping level and implement.
â?¢Appropriate teaching methods and techniques. Thorough knowledge of the subject to be taught and its background.
â?¢Fluency in English,Marathi and Hindi.
â?¢Knowledge of utilizing all the modern teaching aids appropriately and effectively.
â?¢Uncommon ability to create quick interests among the students about the subject.
â?¢Knowledge of common student's psychology and high concern regarding the problems they face in the learning process.
â?¢Follows high standard of personal and work ethics.
â?¢Friendly, approachable and hardworking individual with exceptional interest in providing tutoring services to assist students in comprehending topic related concepts.
â?¢Patient and pleasant, with a demonstrated ability in communicating with people from different backgrounds.
Special talent for:
â?¢ Recognizing variations in student backgrounds, abilities and learning styles.
â?¢ Interacting with students in a friendly and respectful manner, aiming to comprehend their specific learning abilities and limitations.
â?¢Explaining concepts in easy to understand ways without overwhelming students

Languages Spoken

English

Marathi

Hindi

Education

Sydenham college of commerce and economics Pursuing

Bachelor of Banking and Insurance

Address

Taloja Phase 1, Mumbai, India - 410208

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Teaches

Class 6 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 6 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

English, Sanskrit, Social Science, EVS, Mathematics, Marathi, Science, Hindi

ICSE Subjects taught

History, Hindi, Chemistry, EVS, Marathi, Physics, English, Mathematics, Sanskrit, Biology, Geography

Taught in School or College

No

State Syllabus Subjects taught

Social science, Science, English, Mathematics, EVS, Marathi, Hindi, Sanskrit

Class 7 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 7 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

English, Sanskrit, Social Science, EVS, Mathematics, Marathi, Science, Hindi

ICSE Subjects taught

History, Hindi, Chemistry, EVS, Marathi, Physics, English, Mathematics, Sanskrit, Biology, Geography

Taught in School or College

No

State Syllabus Subjects taught

Social science, Science, English, Mathematics, EVS, Marathi, Hindi, Sanskrit

Class 8 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 8 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

English, Sanskrit, Social Science, EVS, Mathematics, Marathi, Science, Hindi

ICSE Subjects taught

History, Hindi, Chemistry, EVS, Marathi, Physics, English, Mathematics, Sanskrit, Biology, Geography

Taught in School or College

No

State Syllabus Subjects taught

Social science, Science, English, Mathematics, EVS, Marathi, Hindi, Sanskrit

Class 9 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 9 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

Hindi, Science, Social science, Mathematics, Elements of business, Accountancy, Information and Comunication Technology, English, Sanskrit, Marathi

ICSE Subjects taught

Hindi, English, Physics, Economic Application, Biology, EVS, Mathematics, Geography, Chemistry, History and Civics

Taught in School or College

No

State Syllabus Subjects taught

EVS, Hindi, Science, Marathi, English, Social Science, Mathematics, Sanskrit

Class 10 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 10 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

Hindi, Science, Social science, Mathematics, Elements of business, Accountancy, Information and Comunication Technology, English, Sanskrit, Marathi

ICSE Subjects taught

Hindi, English, Physics, Economic Application, Biology, EVS, Mathematics, Geography, Chemistry, History and Civics

Taught in School or College

No

State Syllabus Subjects taught

EVS, Hindi, Science, Marathi, English, Social Science, Mathematics, Sanskrit

Class I-V Tuition
1 Student

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class I-V Tuition

11

Board

CBSE, State, ICSE

State boards taught

Maharashtra State Board

CBSE Subjects taught

EVS, English, Hindi, Mathematics, Science, Marathi, Computers

ICSE Subjects taught

Hindi, EVS, English, Social Studies, Science, Mathematics, Marathi

Experience in School or College

1year experience in MOONSTAR GLOBAL SCHOOL.i taught Marathi and Hindi there

Taught in School or College

Yes

State Syllabus Subjects taught

Marathi, Science, Hindi, Mathematics, EVS, Social Science, English

Nursery-KG Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Nursery-KG Tuition

2

Subject

EVS, English, Drawing, Mathematics

Taught in School or College

No

BCom Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in BCom Tuition

2

BCom Subject

Financial Markets and Institutions, Public relations and Corporate Communication, Office Management and Secretarial Practice, Risk Management, E-Commerce, Auditing and Corporate Governance, International Business, Company Law, Business Taxation, Corporate Accounting, Financial Accounting, Business Mathematics and Statistics, Advertising, International Finance, Investment Analysis, Portfolio Management & Wealth Management, Information Technology and Audit, Human Resource Management, Business Organisation and Management, Banking Law and Operation, Business Ethics, Banking Technology and Management, Accounting Information Systems, Stock and Commodity Markets, Event Management, Marketing, Personal Selling and Salesmanship, Business Communication, Financial Management, Micro & Macro Economics, Cost Accounting, Financial Analysis and Reporting, Banking and Insurance, Organisational Behaviour, Business Laws, International Banking & Forex Management, Retail Management, Management Accounting

Type of class

Regular Classes, Crash Course

Business Communication Language

English, Hindi

Class strength catered to

Group Classes

Taught in School or College

No

Class 12 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 12 Tuition

2

Board

State, CBSE

CBSE Subjects taught

English, Accountancy, Economics, Mathematics, Hindi

Taught in School or College

No

State Syllabus Subjects taught

Economics, Hindi, Business Studies, Secretarial Practices , Accountancy, English, Statistics, Marathi, Mathematics, Organisation of Commerce

Class 11 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 11 Tuition

2

Board

State, CBSE

CBSE Subjects taught

English, Accountancy, Economics, Mathematics, Hindi

Taught in School or College

No

State Syllabus Subjects taught

Hindi, Business Studies, Secretarial Practices , Accountancy, English, Statistics, Education, Marathi, Mathematics, Organisation of Commerce

Reviews

No Reviews yet!

FAQs

1. Which school boards of Class 8 do you teach for?

CBSE, ICSE, State

2. Have you ever taught in any School or College?

No

3. Which classes do you teach?

I teach BCom Tuition, Class 10 Tuition, Class 11 Tuition, Class 12 Tuition, Class 6 Tuition, Class 7 Tuition, Class 8 Tuition, Class 9 Tuition, Class I-V Tuition and Nursery-KG Tuition Classes.

4. Do you provide a demo class?

Yes, I provide a paid demo class.

5. How many years of experience do you have?

I have been teaching for 2 years.

Contact

Answers by Ashwini R. (8)

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +2 CBSE/Class 1/Maths CBSE/Class 9/Mathematics

What's the 'I love you' math problem?

Is this what you are looking for? i <3 u <3 means heart. So it is read as I love you. This relation can be brought down by simple algebra like, say, i+5 < 3u+5 => i<3u The famous style is this, Solve for i, 9x- 7i < 3 (3x -7u) = 9x - 7i < 9x - 21u = -7i < -21u... ...more

Is this what you are looking for?

i <3 u

 

<3 means heart. So it is read as I love you.

 

This relation can be brought down by simple algebra like,

say, i+5 < 3u+5 => i<3u

The famous style is this,

 

Solve for i,

9x- 7i < 3 (3x -7u)

= 9x - 7i < 9x - 21u

= -7i < -21u (cancel out the 9x)

simplified: i <3 u !

therefore: I love you

Answers 2 Comments
Dislike Bookmark

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +2 CBSE/Class 1/Maths CBSE/Class 9/Mathematics

How do geniuses study math?

elekinetically. Jokes aside, I know a people who are excellent at Math and some can definitely be classified as genius. What they do is understand the concept rather than learn how to simply answer the question. This way you’d be surprised that they will figure out extensions of that math question... ...more

elekinetically. Jokes aside, I know a people who are excellent at Math and some can definitely be classified as genius. What they do is understand the concept rather than learn how to simply answer the question.

 

This way you’d be surprised that they will figure out extensions of that math question without even properly studying it. The reason is that their concept is so strong and when they link that with their already capable logic the result is a quick and thorough understanding of the topic.

Answers 5 Comments
Dislike Bookmark

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +2 CBSE/Class 1/Maths CBSE/Class 9/Mathematics

Why do we have to estimate for every math problem?

When we estimate, we find an answer that is close to, but not exactly, the accurate answer for a problem.
Answers 5 Comments
Dislike Bookmark

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +2 CBSE/Class 1/Maths CBSE/Class 9/Mathematics

What is a solution to the problem x^3 + ln(x+1) =8?

The function f(x)=x3+ln(x+1) is defined over (−1,∞) . The limit at −1 is −∞ , the limit at ∞ is ∞ . The derivative is f′(x)=3x2+1x+1>0 so you know that the function is strictly increasing. Therefore the given equation has a single solution.... ...more

The function f(x)=x3+ln(x+1) is defined over (−1,∞) . The limit at −1 is −∞ , the limit at ∞ is ∞ . The derivative is

 

f′(x)=3x2+1x+1>0 

 

so you know that the function is strictly increasing. Therefore the given equation has a single solution. Since f(2)>8 and f(1)<8 , the solution is inside the interval (1,2) .

 

You can determine an approximation with the desired accuracy with numerical methods.

Answers 1 Comments
Dislike Bookmark

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +1 CBSE/Class 9/Mathematics

How can I prove that if y=(x^n)logx, then yn+1=n!/x?

I assume that, by ‘yn+1’, you mean the (n+1)th derivative of y with respect to x - this is often written (with the parentheses) as a superscript, e.g. y(n+1) In other words, you want to prove that: ddxn+1(xnln(x))=n!x I suggest that you edit the question to make your meaning... ...more

I assume that, by ‘yn+1’, you mean the (n+1)th derivative of y with respect to x - this is often written (with the parentheses) as a superscript, e.g.

 

y(n+1) 

 

In other words, you want to prove that:

 

ddxn+1(xnln(x))=n!x 

 

I suggest that you edit the question to make your meaning clearer as, from the two answers submitted before mine, they didn’t understand you.

 

 

 

This doesn’t really count as a proof, but I think its a way to demonstrate why this is true.

 

From the product rule for differentiation,

 

dydx=xnddxln(x)+ln(x)ddxxn 

 

=xnx+nxn−1ln(x)=xn−1+nxn−1ln(x) 

 

Having differentiated once, we still have to differentiate a further n times.

 

dn+1ydxn+1=dndxn(xn−1+nxn−1ln(x)) 

 

From the sum rule for differentiation, we can split this into two parts:

 

dndxnxn−1+ndndxnxn−1ln(x) 

 

Let’s look at the first part. When we differentiate an expression than contains a term that is a power of x, we reduce the power by 1. So, if we differentiate xb b times, we end up with a constant [ xb−b=x0 ], and if we differentiate again, we get a zero. In this case, we’re wanting to differentiate xn−1 n times, this means that the term eventually becomes zero. So, our problem simplifies to:

 

ndndxnxn−1ln(x)=ndn−1dxn−1(ddxxn−1ln(x)) 

 

Applying the product rule again:

 

=ndn−1dxn−1(xn−2+(n−1)xn−2ln(x)) 

 

Applying the sum rule again, the first term again reduces to zero with continued differentiation, so we are left with:

 

ndn−1dxn−1(n−1)xn−2ln(x) 

 

As (n−1) is a constant, we can move it outside the differentiation; I’ll also introduce the notation n[2]=n!(n−2)! 

 

So, we have:

 

n[2]dn−1dxn−1xn−2ln(x) 

 

Applying the product rule again:

 

n[2]dn−2dxn−2(xn−3+(n−2)xn−3ln(x)) 

 

Applying the sum rule again, the first term again reduces to zero with continued differentiation, so we are left with:

 

n[3]dn−2dxn−2xn−3ln(x) 

 

Continuing the pattern we get:

 

n[4]dn−3dxn−3xn−4ln(x) 

 

n[5]dn−4dxn−4xn−5ln(x) 

 

…

 

n[n−1]d2dx2x1ln(x) 

 

n[n]ddxln(x)=n[n]x 

 

As the coefficient is just n! , our answer is:

 

n!x 

 

 

Answers 2 Comments
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Contact

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Teaches

Class 6 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 6 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

English, Sanskrit, Social Science, EVS, Mathematics, Marathi, Science, Hindi

ICSE Subjects taught

History, Hindi, Chemistry, EVS, Marathi, Physics, English, Mathematics, Sanskrit, Biology, Geography

Taught in School or College

No

State Syllabus Subjects taught

Social science, Science, English, Mathematics, EVS, Marathi, Hindi, Sanskrit

Class 7 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 7 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

English, Sanskrit, Social Science, EVS, Mathematics, Marathi, Science, Hindi

ICSE Subjects taught

History, Hindi, Chemistry, EVS, Marathi, Physics, English, Mathematics, Sanskrit, Biology, Geography

Taught in School or College

No

State Syllabus Subjects taught

Social science, Science, English, Mathematics, EVS, Marathi, Hindi, Sanskrit

Class 8 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 8 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

English, Sanskrit, Social Science, EVS, Mathematics, Marathi, Science, Hindi

ICSE Subjects taught

History, Hindi, Chemistry, EVS, Marathi, Physics, English, Mathematics, Sanskrit, Biology, Geography

Taught in School or College

No

State Syllabus Subjects taught

Social science, Science, English, Mathematics, EVS, Marathi, Hindi, Sanskrit

Class 9 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 9 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

Hindi, Science, Social science, Mathematics, Elements of business, Accountancy, Information and Comunication Technology, English, Sanskrit, Marathi

ICSE Subjects taught

Hindi, English, Physics, Economic Application, Biology, EVS, Mathematics, Geography, Chemistry, History and Civics

Taught in School or College

No

State Syllabus Subjects taught

EVS, Hindi, Science, Marathi, English, Social Science, Mathematics, Sanskrit

Class 10 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 10 Tuition

2

Board

CBSE, ICSE, State

CBSE Subjects taught

Hindi, Science, Social science, Mathematics, Elements of business, Accountancy, Information and Comunication Technology, English, Sanskrit, Marathi

ICSE Subjects taught

Hindi, English, Physics, Economic Application, Biology, EVS, Mathematics, Geography, Chemistry, History and Civics

Taught in School or College

No

State Syllabus Subjects taught

EVS, Hindi, Science, Marathi, English, Social Science, Mathematics, Sanskrit

Class I-V Tuition
1 Student

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class I-V Tuition

11

Board

CBSE, State, ICSE

State boards taught

Maharashtra State Board

CBSE Subjects taught

EVS, English, Hindi, Mathematics, Science, Marathi, Computers

ICSE Subjects taught

Hindi, EVS, English, Social Studies, Science, Mathematics, Marathi

Experience in School or College

1year experience in MOONSTAR GLOBAL SCHOOL.i taught Marathi and Hindi there

Taught in School or College

Yes

State Syllabus Subjects taught

Marathi, Science, Hindi, Mathematics, EVS, Social Science, English

Nursery-KG Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Nursery-KG Tuition

2

Subject

EVS, English, Drawing, Mathematics

Taught in School or College

No

BCom Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in BCom Tuition

2

BCom Subject

Financial Markets and Institutions, Public relations and Corporate Communication, Office Management and Secretarial Practice, Risk Management, E-Commerce, Auditing and Corporate Governance, International Business, Company Law, Business Taxation, Corporate Accounting, Financial Accounting, Business Mathematics and Statistics, Advertising, International Finance, Investment Analysis, Portfolio Management & Wealth Management, Information Technology and Audit, Human Resource Management, Business Organisation and Management, Banking Law and Operation, Business Ethics, Banking Technology and Management, Accounting Information Systems, Stock and Commodity Markets, Event Management, Marketing, Personal Selling and Salesmanship, Business Communication, Financial Management, Micro & Macro Economics, Cost Accounting, Financial Analysis and Reporting, Banking and Insurance, Organisational Behaviour, Business Laws, International Banking & Forex Management, Retail Management, Management Accounting

Type of class

Regular Classes, Crash Course

Business Communication Language

English, Hindi

Class strength catered to

Group Classes

Taught in School or College

No

Class 12 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 12 Tuition

2

Board

State, CBSE

CBSE Subjects taught

English, Accountancy, Economics, Mathematics, Hindi

Taught in School or College

No

State Syllabus Subjects taught

Economics, Hindi, Business Studies, Secretarial Practices , Accountancy, English, Statistics, Marathi, Mathematics, Organisation of Commerce

Class 11 Tuition

Class Location

Online (video chat via skype, google hangout etc)

Student's Home

Tutor's Home

Years of Experience in Class 11 Tuition

2

Board

State, CBSE

CBSE Subjects taught

English, Accountancy, Economics, Mathematics, Hindi

Taught in School or College

No

State Syllabus Subjects taught

Hindi, Business Studies, Secretarial Practices , Accountancy, English, Statistics, Education, Marathi, Mathematics, Organisation of Commerce

No Reviews yet!

Answers by Ashwini R. (8)

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +2 CBSE/Class 1/Maths CBSE/Class 9/Mathematics

What's the 'I love you' math problem?

Is this what you are looking for? i <3 u <3 means heart. So it is read as I love you. This relation can be brought down by simple algebra like, say, i+5 < 3u+5 => i<3u The famous style is this, Solve for i, 9x- 7i < 3 (3x -7u) = 9x - 7i < 9x - 21u = -7i < -21u... ...more

Is this what you are looking for?

i <3 u

 

<3 means heart. So it is read as I love you.

 

This relation can be brought down by simple algebra like,

say, i+5 < 3u+5 => i<3u

The famous style is this,

 

Solve for i,

9x- 7i < 3 (3x -7u)

= 9x - 7i < 9x - 21u

= -7i < -21u (cancel out the 9x)

simplified: i <3 u !

therefore: I love you

Answers 2 Comments
Dislike Bookmark

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +2 CBSE/Class 1/Maths CBSE/Class 9/Mathematics

How do geniuses study math?

elekinetically. Jokes aside, I know a people who are excellent at Math and some can definitely be classified as genius. What they do is understand the concept rather than learn how to simply answer the question. This way you’d be surprised that they will figure out extensions of that math question... ...more

elekinetically. Jokes aside, I know a people who are excellent at Math and some can definitely be classified as genius. What they do is understand the concept rather than learn how to simply answer the question.

 

This way you’d be surprised that they will figure out extensions of that math question without even properly studying it. The reason is that their concept is so strong and when they link that with their already capable logic the result is a quick and thorough understanding of the topic.

Answers 5 Comments
Dislike Bookmark

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +2 CBSE/Class 1/Maths CBSE/Class 9/Mathematics

Why do we have to estimate for every math problem?

When we estimate, we find an answer that is close to, but not exactly, the accurate answer for a problem.
Answers 5 Comments
Dislike Bookmark

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +2 CBSE/Class 1/Maths CBSE/Class 9/Mathematics

What is a solution to the problem x^3 + ln(x+1) =8?

The function f(x)=x3+ln(x+1) is defined over (−1,∞) . The limit at −1 is −∞ , the limit at ∞ is ∞ . The derivative is f′(x)=3x2+1x+1>0 so you know that the function is strictly increasing. Therefore the given equation has a single solution.... ...more

The function f(x)=x3+ln(x+1) is defined over (−1,∞) . The limit at −1 is −∞ , the limit at ∞ is ∞ . The derivative is

 

f′(x)=3x2+1x+1>0 

 

so you know that the function is strictly increasing. Therefore the given equation has a single solution. Since f(2)>8 and f(1)<8 , the solution is inside the interval (1,2) .

 

You can determine an approximation with the desired accuracy with numerical methods.

Answers 1 Comments
Dislike Bookmark

Answered on 11/12/2021 Learn CBSE/Class 10/Mathematics +1 CBSE/Class 9/Mathematics

How can I prove that if y=(x^n)logx, then yn+1=n!/x?

I assume that, by ‘yn+1’, you mean the (n+1)th derivative of y with respect to x - this is often written (with the parentheses) as a superscript, e.g. y(n+1) In other words, you want to prove that: ddxn+1(xnln(x))=n!x I suggest that you edit the question to make your meaning... ...more

I assume that, by ‘yn+1’, you mean the (n+1)th derivative of y with respect to x - this is often written (with the parentheses) as a superscript, e.g.

 

y(n+1) 

 

In other words, you want to prove that:

 

ddxn+1(xnln(x))=n!x 

 

I suggest that you edit the question to make your meaning clearer as, from the two answers submitted before mine, they didn’t understand you.

 

 

 

This doesn’t really count as a proof, but I think its a way to demonstrate why this is true.

 

From the product rule for differentiation,

 

dydx=xnddxln(x)+ln(x)ddxxn 

 

=xnx+nxn−1ln(x)=xn−1+nxn−1ln(x) 

 

Having differentiated once, we still have to differentiate a further n times.

 

dn+1ydxn+1=dndxn(xn−1+nxn−1ln(x)) 

 

From the sum rule for differentiation, we can split this into two parts:

 

dndxnxn−1+ndndxnxn−1ln(x) 

 

Let’s look at the first part. When we differentiate an expression than contains a term that is a power of x, we reduce the power by 1. So, if we differentiate xb b times, we end up with a constant [ xb−b=x0 ], and if we differentiate again, we get a zero. In this case, we’re wanting to differentiate xn−1 n times, this means that the term eventually becomes zero. So, our problem simplifies to:

 

ndndxnxn−1ln(x)=ndn−1dxn−1(ddxxn−1ln(x)) 

 

Applying the product rule again:

 

=ndn−1dxn−1(xn−2+(n−1)xn−2ln(x)) 

 

Applying the sum rule again, the first term again reduces to zero with continued differentiation, so we are left with:

 

ndn−1dxn−1(n−1)xn−2ln(x) 

 

As (n−1) is a constant, we can move it outside the differentiation; I’ll also introduce the notation n[2]=n!(n−2)! 

 

So, we have:

 

n[2]dn−1dxn−1xn−2ln(x) 

 

Applying the product rule again:

 

n[2]dn−2dxn−2(xn−3+(n−2)xn−3ln(x)) 

 

Applying the sum rule again, the first term again reduces to zero with continued differentiation, so we are left with:

 

n[3]dn−2dxn−2xn−3ln(x) 

 

Continuing the pattern we get:

 

n[4]dn−3dxn−3xn−4ln(x) 

 

n[5]dn−4dxn−4xn−5ln(x) 

 

…

 

n[n−1]d2dx2x1ln(x) 

 

n[n]ddxln(x)=n[n]x 

 

As the coefficient is just n! , our answer is:

 

n!x 

 

 

Answers 2 Comments
Dislike Bookmark

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Ashwini R. describes herself as Ace Tutor. She conducts classes in BCom Tuition, Class 10 Tuition and Class 11 Tuition. Ashwini is located in Taloja Phase 1, Mumbai. Ashwini takes Regular Classes- at her Home. She has 11 years of teaching experience . Ashwini is pursuing Bachelor of Banking and Insurance from Sydenham college of commerce and economics. She is well versed in English, Marathi and Hindi.

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