What is the chain rule?

The chain rule is a technique used when differentiating. It is needed when differentiating composite functions, i.e. when y = f(g(x)).For example, y = sin(x^3) is a composite function, where (referring to the general formula above) f(x) = sin(x), g(x) = x^3.The general form of the chain rule is dy/dx = g'(x) x f'(g(x)), i.e. you differentiate the inside function then multiply it by the differential of the whole function.Using the example from above: y = sin(x^3) dy/dx = 3x^2 x cos(x^3)Reverse chain rule can be used to quickly integrate a function if it is spotted.For example, if you were given the function y = 3x^2 x cos(x^3) to integrate, you may just integrate by parts or you may spot that it will be sin(x^3), by reverse chain rule.

Answered by Maths tutor

2720 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Prove that f(x) the inverse function of g(x) where f(x)= - 3x–6 and g(x)= - x/3–2


Solve the equation 3sin^2(x) + sin(x) + 8 = 9cos^2(x), -180<X<180. Then find smallest positive solution of 3sin^2(2O-30) + sin(2O-30) + 8 = 9cos^2(2O-30).


How do I integrate by parts?


Express 9^(3x+)1 in the form 3^y giving y in the form of ax+b where a and b are constants.


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