What is the Product Rule?

The product rule is used when differentiating two functions that are multiplied by eachother. The formula for the product rule is: 

U (dv/dx) + V (du/dx)    where 'dv/dx' is the differential of the function, V.

For example: 

y=(x2 + 3)(2x +5) .... we label the first bracket as U and the second as V.

To find dy/dx we apply the product rule:

U= (x2 + 3)      du/dv= 2x as we differentiate any x variable by bringing the power down to the front and then minusing                                       one from the power)

V= (2x+5)        dv/dx= 2

Therefore, applying the product rule gives: 

(x2 +3)2 + 2x(2x+5) = 4x2 + 10x + 6

AW
Answered by Abbie W. Maths tutor

3050 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate the function f(x) = 1/(4x-1)


Find the location and nature of the turning point of the line y=-x^2+3x+2


a) i) find dy/dx of y = 3x^4 - 8x^3 - 3 ii) then find d^2y/dx^2 b) verify that x=2 at a stationary point on the curve c c) is this point a minima or a maxima


Differentiate x^3 − 3x^2 − 9x. Hence find the x-coordinates of the stationary points on the curve y = x^3 − 3x^2 − 9x


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