MYTUTOR SUBJECT ANSWERS

564 views

What is the chain rule, product rule and quotient rule and when do I use them?

The chain rule, product rule and quotient rule are all 3 methods of differentiating complex functions.

Chain rule

The chain rule is as follows: (dy/dx) = (dy/dz).(dz/dx) or D{f(g(x))}/dx = f'(g(x)).g'(x)

The chain rule is used when you want to differentiate a function to the power of a number. For example, you would use it to differentiate (4x^3 + 3x)^5

The chain rule is also used when you want to differentiate a function inside of another function. For example, you would use it to differentiate sin(3x) (With the function 3x being inside the sin() function)

Product rule

The product rule is as follows d(f(x).g(x))/dx = g(x).f'(x) + f(x).g'(x)

The product rule is used when you want to differentiate two different functions multiplied together. For example, you would use it to differentiate (x^4 + 7x + 2)(3x^2 + 1)

Quotient rule

The Quotient rule is as follows: d(f(x) / g(x))/dx = (f'(x)g(x) - g(x)f'(x)) / g(x)^2

The Quotient rule is used when you want to differentiate one function divided by another. For example, you would use it to differentiate (4x + 5)/(3 - x^2)

Hakeem K. A Level Maths tutor, A Level Further Mathematics  tutor, GC...

2 years ago

Answered by Hakeem, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

258 SUBJECT SPECIALISTS

£26 /hr

Victor T.

Degree: Economics (Bachelors) - Cambridge University

Subjects offered: Maths, Economics+ 2 more

Maths
Economics
-Personal Statements-
-Oxbridge Preparation-

“Hi I'm Victor and I am a second-year economist at Cambridge having achieved a First last year. I very much enjoy teaching and my aim to instil my passion and enthusiasm for Maths and Economics in my students. I got 12 A*s at GCSE and 5...”

£20 /hr

Oscar G.

Degree: Economics and Politics (Bachelors) - Bristol University

Subjects offered: Maths, Politics+ 1 more

Maths
Politics
Economics

“About Me: I am a Economics and Politics student at Bristol University. I have always had a real passion and love for all things involving Mathematics, Economics and Politics and hope that my tutorials will instill that love in you, to...”

MyTutor guarantee

£20 /hr

Laura W.

Degree: Materials Science MEng (Masters) - Oxford, Trinity College University

Subjects offered: Maths, Science+ 5 more

Maths
Science
Further Mathematics
Extended Project Qualification
Chemistry
.PAT.
-Oxbridge Preparation-

“Enthusiastic Oxford student ready to improve your understanding of the Physical Sciences.”

MyTutor guarantee

About the author

Hakeem K.

Currently unavailable: for regular students

Degree: Mathematics And Computer Science (Masters) - Bristol University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Friendly first-year Mathematics and Computer science tutor ready to turn 'nay' grades into A-grades!”

You may also like...

Other A Level Maths questions

Find the tangent to the curve y=x^3+3 at the point x=1.

Integrate 4x^3 + 6x^2 +4x + 3

How do I find the minimum or maximum of a quadratic function?

Differentiate: y=12x(2x+1)+1/x

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok