MYTUTOR SUBJECT ANSWERS

780 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 -...

2 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

323 SUBJECT SPECIALISTS

£26 /hr

Priya L.

Degree: Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Economics

“My goal is to elevate the confidence of students by ensuring they truly understand Maths at GCSE and A Level”

£20 /hr

John W.

Degree: Mathematics (Masters) - St. Andrews University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I've done a broad range of maths learning and tutoring over the years, now continuing this on to university I'm sure I'll be able to help you out!”

£20 /hr

Katie W.

Degree: Mathematics (Bachelors) - Exeter University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Animated Mathematics student with 2 years experience of GCSE maths tutoring (AQA). I have a personal interest in the connections between maths and music.”

About the author

Tully K.

Currently unavailable: no new students

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

Subjects offered:Maths, .PAT.+ 1 more

Maths
.PAT.
-Oxbridge Preparation-

“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

You may also like...

Other A Level Maths questions

Solve simultaneously: x + y + 3 = 0 and y = 2x^2 +3x - 1

How do you find the roots of a cubic equation?

Write down the values of (1) loga(a) and (2) loga(a^3) [(1) log base a, of a (2) log base a of (a^3)]

The variable x=t^2 and the variable y=2t. What is dy/dx in terms of t?

View A Level Maths tutors

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

mtw:mercury1:status:ok