Differentiate y = 2xln(x)

This is an example of a question where you would use the product rule, where if y = uv then dy/dx = udv/dx + vdu/dx. In this case u = 2x and v = ln(x). So first of all we will differentiate 2x which is fairly easy and is equal to 2 and then we will differentiate ln(x) which is slightly harder and equal to 1/x, this is one that you will have to learn by heart.
Now that we have the differentials of 2x and ln(x) we can put it all together to find the differential of y. So by using the product rule from earlier dy/dx = 2x*(1/x) + ln(x)*2 which when we simplify is equal to 2( 1+ln(x) ).

Answered by Toby W. Maths tutor

6441 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How would I find a the tangent of a point on a line?


How can we calculate the derivative of function f(x)= (x+2)/(x-1)?


Three forces, (15i + j) N, (5qi – pj) N and (–3pi – qj) N, where p and q are constants, act on a particle. Given that the particle is in equilibrium, find the value of p and the value of q. (Mechanics 1 June 2017)


Use Implicit Differentiation to find dy/dx of the following equation: 3(x)^2 + 8xy + 5(y)^2 = 4


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