Given that y=(4x+1)^3sin 2x , find dy/dx .

So this function is the product of two functions of x, so we use the product rule to differentiate it. The rule states if y=uv, dy/dx=(du/dx)v+(dv/dx)u. In this function we assign u=(4x+1)3 and v=sin2x. When we differentiate u we need to use the chain rule, as there is a function within a function, which gives us (3(4x+1)2)x4 which is equal to 12(4x+1)2. When we differentiate v we get 2cos2x, again using chain rule. So we plug these values into the formula which gives us dy/dx=12(4x+1)2Sin2x + 2(4x+1)3Cos2x

TF
Answered by Tom F. Maths tutor

6179 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Determine whether the line with equation 2x+ 3y + 4 = 0 is parallel to the line through the points with coordinates (9, 4) and (3, 8).


A curve has the equation y=7-2x^5, find dy/dx of this curve


Compare the following logarithms in base 1/2 without a calculator: log(8) and log(512)


Solve the equation 2y^(1/2) -7y^(1/4) +3 = 0


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