How would you differentiate f(x) = 2x(3x - 1)^2 using the chain rule?

In order to differentiate this expression, you need to use the chain rule. 

The chain rule gives: f'(x) = uv' + u'v.

The u and the v are two parts of the original function f(x). The apostrophe ' at the end means the derivative of that.

We need to assign values to u and v, so we look at the function f(x) = 2x(3x - 1)2 to see what parts it is in:

u = 2x

v = (3x - 1)2

Then, we differentiate each of these.

u' = 2

v' = 2 x 3 x (3x - 1)1 = 6(3x - 1)

Now, we can put this expression altogether:

f'(x) = uv' + u'v = 2x(6(3x - 1)) + 2(3x - 1)2

And now, simplify.

f'(x) = 12x(3x - 1) + 2(3x - 1)2

f'(x) = 2(3x - 1)[6x + (3x - 1)]

f'(x) = 2(3x - 1)(9x - 1)

f'(x) = 2(27x2 - 9x - 3x + 1)

f'(x) = 2(27x2 - 12x + 1)

f'(x) = 54x2 - 24x + 2

Sam E. A Level Maths tutor, GCSE Maths tutor

2 weeks ago

Answered by Sam, an A Level Maths tutor with MyTutor

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


Julia L. A Level Maths tutor, A Level Economics tutor, A Level Russia...
View profile
£22 /hr

Julia L.

Degree: Economics L100 (Bachelors) - Durham University

Subjects offered: Maths, Sociology+ 2 more


“Hi! My name is Julia, and I am Durham University student. I have just been through the stress of A level exams - I've been in your shoes, so now, my goal is to make your exam time as smooth and painless as it can be. I can help you wi...”

Robert L. GCSE Maths tutor, A Level Maths tutor, GCSE Geography tutor...
View profile
£20 /hr

Robert L.

Degree: Geophysics (Masters) - University College London University

Subjects offered: Maths, Physics+ 1 more


“Hi, my name is Robert and I'm studying Geophysics at University College London, currently in my second year, with an interest in hazard and disaster reduction. Having been tutored myself in the past I know the importance of an underst...”

MyTutor guarantee

Jonathon V. A Level Maths tutor, GCSE Maths tutor, 13 plus  Maths tut...
View profile
£30 /hr

Jonathon V.

Degree: Maths & Physics (Bachelors) - Exeter University

Subjects offered: Maths, Physics+ 1 more

Further Mathematics

“Hi I'm graduating this July with a 1st in Maths and Physics from Exeter University. I'm going to be starting my physics PhD in September and looking to do some tutoring alongside my postgraduate studies.  Having done my A levels no t...”

MyTutor guarantee

About the author

Sam E. A Level Maths tutor, GCSE Maths tutor
View profile
£20 /hr

Sam E.

Degree: Computer Science (Masters) - York University

Subjects offered: Maths


“About me: Hello! I'm a first year Computer Science student at the University of York. I offer tutoring for maths at GCSE and A-Level. Despite not studying maths now, it was my original love - the subject which first taught me how to e...”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Two lines have equations r = (1,4,1)+s(-1,2,2) and r = (2,8,2)+t(1,3,5). Show that these lines are skew.

Find the derivative of x^x

Find the inverse of f(x) = (3x - 6)/2

Integrate the following function by parts and reduce it to it's simplest form. f(x) = ln(x).

View A Level Maths tutors


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