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

Answered by Tom F. Maths tutor

6139 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using the equation cos(a+b) = cos(a)cos(b) - sin(a)sin(b) or otherwise, show that cos(2x) = 2cos^2(x) - 1.


Locate the position and the nature of any turning points in the function: 2x^3 - 9x^2 +12x


A cup of coffee is cooling down in a room following the equation x = 15 + 70e^(-t/40). Find the rate at which the temperature is decreasing when the coffee cools to 60°C.


Problem of Optimisation: A company is designing a logo. The logo is a circle of radius 4 inches with an inscribed rectangle. The rectangle must be as large as possible.


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