Differentiate sin(x^3) with respect to y

For this we must use the chain rule. We start by defining x3 as a new variable, u = x3 Can then rewrite the expression as y = sin(u) Chain rule tells us that dy/dx = (dy/du)(du/dx) We can calculate these individidually. dy/du = cos(u)  du/dx = 3x2 Finally we can then say, dy/dx = dy/du * du/dx = cos(u) * 3x2 = 3x2cos(x3)

LB
Answered by Lloyd B. Maths tutor

6191 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

An open-topped fish tank is to be made for an aquarium. It will have a square base, rectangular sides, and a volume of 60 m3. The base materials cost £15 per m2 and the sides £8 per m2. What should the height be to minimise costs?


How to differentiate e^x . sin(x)


Given the points P(-1,1) and S(2,2), give the equation of the line passing through P and perpendicular to PS.


What is the chain rule?


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