Given f(x) = (x^4 - 1) / (x^4 + 1), use the quotient rule to show that f'(x) = nx^3 / (x^4 + 1)^2 where n is an integer to be determined.

QUOTIENT RULE: [u(x) / v(x)]' = [u'(x)v(x) - u(x)v'(x)] / v2We have: u(x) = x4 - 1, hence u'(x) = 4x3v(x) = x4 + 1, hence v'(x) = 4x3So we have: [(4x3)(x4 + 1) - (4x3)(x4 - 1)] / (x4 + 1)2Expanding gives us: [4x7 + 4x3 - 4x7 + 4x3] / (x4 + 1)2Giving us a final answer of: [8x3] / (x4 + 1)2, and hence the integer n = 8

TA
Answered by Thomas A. Maths tutor

2927 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the equation 3sin^2(x) + sin(x) + 8 = 9cos^2(x), -180<X<180. Then find smallest positive solution of 3sin^2(2O-30) + sin(2O-30) + 8 = 9cos^2(2O-30).


What's the point of Maths?


I don't understand how functions work. How do I decide if something is a function?


When would you apply the product rule in differentiation and how do you do this?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning