differentiate: y=[xcos(x^3)]/[(x^4 + 1)^3] with respect to x

This question is on the trickier side as it is heavily computational and requires a good knowledge of the differentiation rules however it is a good way to practise using multiple rules at once.First we will use the quotient rule formula: dy/dx = [vdu-udv]/[v2]we will set: u = xcos(x3) and v = (x4+1)3by using the product and chain rule we can the calculate du = cos(x3) - 3x3sin(x3) and dv = 12x3(x4 + 1)2substituting these values into the quotient rule formula we get: dy/dx = { (x4 + 1)3[cos(x3) - 3x3sin(x3)] - 12x4cos(x3)(x4 + 1)2 }/{(x4 + 1)6}Finally, after simplifying we achieve: dy/dx = { cos(x3)(1 - 11x4) - 3x2sin(x3)(1 + x5) }/{(x4 + 1)4}

Answered by Elizabeth W. Maths tutor

2304 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate y = x^2 - 2x-3 + e^3x + 2ln(x)


4^x - 2^x+1 - 15 = 0


Find the area bounded by the curve x^2-2x+3 between the limits x=0 and x=1 and the horizontal axis.


What is (5+3i)*(3+5i)


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