Differentiate: 2(x^2+2)^3

This is a chain rule question. Unlike in ordinary differentiation we have more than just the single term 'x' with coefficient 1 raised to the power of something. e.g. x^3 Therefore, there is more steps. We can rewrite the question as 2u^3 with u=x^2+2 as this is more familiar. You can then do the differentiation in terms of u which gives you 6u^2. Now, the extra step is that we have to also differentiate the u and then multiply this by our other answer. Differentiating u gives us 2x which then multiplied by 6u^2 gives us 12x(u^2) Finally, we can now sub back in u=x^2+2 to make sure our final answer is in terms of one variable only. Therefore our final answer is, 12x((x^2+2)^2)

Answered by Charlotte A. Maths tutor

2830 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find X log(x)=4 Base 10


Using the trigonometric identity (sinx)^2 + (cosx)^2 = 1, show that (secx)^2 = (tanx)^2 + 1 is also a trigonometric identity.


Solve for -pi < x < pi: tanx = 4cotx + 3


Why do I have to add +c when I integrate?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences