What is 'Chain Rule' and why is it useful?

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / What is 'Chain Rule' and why is it useful?

860 views

What is 'Chain Rule' and why is it useful?

The chain rule is most commonly seen in Leibniz's notation, which is as follows:

dz/dx = dz/dy * dy/dx

You can remember it intuitively by thinking of the two 'dy' terms cancelling to leave dz/dx.

So why use the chain rule?

You are used to differentiating equations in the form y = f(x), but say both sides of the equation where functions eg g(y) = f(x) and you had to differentiate the equation with respect to x.

g is a function of y, not x, so you can't simply calculate dg(y)/dx like you can df(x)/dx. Using the chain rule we can express dg(y)/dx as dg(y)/dy * dy/dx. These two terms can be calculated (assuming y is a function of x). This is really what the chain rule is saying: that the derivative of a function composition can be expressed as a product of the respective derivatives.

Another example of when the chain rule might come in useful is in mechanics: Acceleration is defined as the derivative of velocity: dv/dt. Sometimes though it might be useful to integrate acceleration of a distance, x, rather than over time. To eliminate time from this expression we can use the chain rule by saying dv/dt = dv/dx * dx/dt. Then noting that dx/dt is in fact velocity (v = dx/dt) we can write that dv/dt = v * dv/dx thus making acceleration a function only of velocity and position.

Tully K. A Level Maths tutor, GCSE Maths tutor, Uni Admissions Test -...

3 years ago

Answered by Tully, an A Level Maths tutor with MyTutor

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

423 SUBJECT SPECIALISTS

Pankaj K. A Level Physics tutor, GCSE Physics tutor, A Level Maths tu...

View profile

£20 /hr

Pankaj K.

Degree: Physics (Bachelors) - Kings, London University

Subjects offered:Maths, Physics+ 1 more

“Positive, Dedicated, Motivating, Calm, Patient, Understanding, Professional, Organised, Experienced, Focused, Enthusiastic, Passionate”

MyTutor guarantee

| 1 completed tutorial

Save profile

£26 /hr

Daniel M.

Degree: Physics (Bachelors) - Bath University

Subjects offered:Maths, Science+ 4 more

“As a patient, understanding, and industrious tutor, I aim to nourish your child's academic curiosity in a caring, understandable and encouraging manner.”

5.0

73 reviews | 165 completed tutorials

Save profile

Tinashe M. A Level Maths tutor, GCSE Maths tutor, GCSE Chemistry tuto...

View profile

£20 /hr

Tinashe M.

Degree: Chemical Engineering MEng (Integrated Masters) - Newcastle University

Subjects offered:Maths, Chemistry

“I love maths, chemistry and biology and my passion for these subjects is something that will help teach students.”

MyTutor guarantee

Save profile

See more A Level Maths tutors

About the author

View profile

Tully K.

Currently unavailable: no new students

Degree: Engineering Science (Masters) - Oxford, Keble College University

Subjects offered:Maths, .PAT.

“Enthusiastic Engineering undergraduate at Oxford University. I'm passionate about maths and science and like to take a logical approach to these subjects and to tutoring.”

MyTutor guarantee

Save profile

Version:	3.49.9
Build:	5f485a18d000
Time:	2017-09-20T16:11:15Z

MYTUTOR SUBJECT ANSWERS

What is 'Chain Rule' and why is it useful?

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

423 SUBJECT SPECIALISTS

About the author

You may also like...

Other A Level Maths questions

One-to-one help is at your fingertips