How to do the chain rule.

The chain rule is used for functions 'inside' other functions. We have learnt to differentiate functions like x^2, y^20, e^x, -sin(x), and we will use these results in the chain rule. Let's look at an example, f(x) = (2x+1)^(1/3). Notice how we have a function (2x+1) 'inside' of another function (u^(1/3)). The chain rule says that if we have a function f(u) in terms of a function u(x) then df/dx=df/dudu/dx, in other words we differentiate the outside and multiply it by the derivative of the inside. In our example f(u) = u^(1/3) and u(x) = 2x+1. Then df/du = 1/3u^(-2/3) = 1/3*(2x+1)^(-2/3) and du/dx = 2. So df/dx = 21/3(2x+1)^(-2/3)

Answered by Jamie C. Maths tutor

3270 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The points A and B have coordinates (3, 4) and (7, 6) respectively. The straight line l passes through A and is perpendicular to AB. Find an equation for l, giving your answer in the form ax + by + c = 0, where a, b and c are integers.


Find the indefinite integral of Ln(x)


Why is the integral of a function the area?


The curve C has parametric equations x=2cos(t) and y=3cos(2t). Find and expression for dy/dx in terms of t.


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