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)). 

JP
Answered by Jaisal P. Maths tutor

5424 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What's the deal with Integration by Parts?


Of the following 4 equations, 3 of them represent parallel lines. Which is the odd one out?


Solve the simultaneous equations, 2x+y-5=0 and x^2-y^2=3


Show that the integral ∫(1-2 sin^2⁡x)/(1+2sinxcosx) dx = (1/2) ln2 between the limits π/4 and 0. [5 marks]


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