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

3407 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the exact gradient of the curve y = ln(1-cos 2x) at the point with x-coordinate π/6.


Show, by first principles, that the differential of x^2 is 2x.


Given the circumference x^2 - 2x + y^2 = 3, find the position of the center P and the value of the Radius. Then find the intercepts with the y axis and the tangent to the circumference at the positive y intercept.


The first term of an arithmetic series is a and the common difference is d. The 12th term is 66.5 and the 19th term is 98. Write down two equations in a and d then solve these simultaneous equations to find a and d.


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:

© 2026 by IXL Learning