What is the quotient rule and how is it applied?

The quotient rule is a formula used to differentiate fractions that contain terms of x in both the numerator and the denominator (we usually refer to this as f(x)/g(x)).
As it isn't possible to differentiate this by normal methods straight away, we use the quotient rule to allow us to do so. For A-level maths, you only need to know how to use the quotient rule, deriving how it is formed is not necessary. The quotient rule takes the following form:
dy/dx = ((g(x)f'(x) - f(x)g'(x))/g(x)^2
Where f'(x), g'(x) are dy/dx of f(x), g(x) respectively. Therefore differentiating the numerator and the denominator seperately, and then plugging these back into the formula, will yield the result of differentiating a fraction of the form f(x)/g(x).

PH
Answered by Pete H. Maths tutor

5111 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate y=(sin(x))^(2)


Integrate 1/(5-2x) for 3≤x≤4


integrate( x^3+4x^2+3)dx


A block of mass 5kg is at rest on a smooth horizontal table, and connected to blocks of 3kg and 4kg which are hanging by strings via pulleys on either end of the table. Find the acceleration of the system and the tension in each string.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning