How do you differentiate (3x+cos(x))(2+4sin(3x))?

Here we have a product of two things, so we will be using the product rule of differentiation. This is: for y=u(x)v(x), where u(x) and v(x) are funtions of x, dy/dx = u'(x)v(x) + u(x)v'(x). So in this case let u(x) = 3x+cos(x) and let v(x) = 2+4sin(3x). We need to find u'(x). u'(x) = 3-sin(x) as we differentiate u(x). v'(x) = 12cos(3x) as we diferentiate v(x). Then using the product rule sated, dy/dx = (3-sin(x))(2+4sin(3x)) + (3x+cos(x))(12cos(3x)). 

Answered by Jaisal P. Maths tutor

4937 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

I don't understand chain rule for differentiation especially when combined with more complex functions.


Find the area encompassed by y=(3-x)x^2 and y=x(4-x) between x=0 and x=2.


Differentiation: How to use the chain rule


I struggle with modelling with differential equation, is there an easier way of interpreting this type of wordy question?


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