When and how do I use the product rule for differentiation?

As the name suggests, the product rule is used to differentiate a function in which a product of 2 expressions in x exists. This means the two expressions in x are multiplied by each other, even when the function is expressed in its simplest form. An example would be y=x3e2x. The product rule is written by generalising one expression in x as u and the other as v: 

If y=u*v then

dy/dx= udv/dx + vdu/dx

This means that, to dfferentiate, we multiply each expression in x by the derivative of the other and add the results. This is illustrated by the example below: 

 y=x3e2x

let u= x3                 v=e2x

du/dx = 3x2            dv/dx= 2e2x

for this example: 

                       dy/dx = u dv/dx + v du/dx

                                = x3*2e2x +  e2x*3x2 

                                = e2x(2x3 + 3x2)

Answered by Rachel T. Maths tutor

10827 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do we know that the derivative of x^2 is 2x?


The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.


Integrate xsin2x


Solve the simultaneous equations y+4x+1 = 0 and y^2+5x^2+2x = 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