How do you differentiate using the chain rule?

The chain rule is used where the equation you are looking to differentiate is a function that is itself raised to a power. For example, we might have y = (x2-2)3 and want to differentiate with respect to x to give dy/dx = ?We could multiply this out to give a full equation, but this can be messy especially if the outside power (3 in the above example) is high. Instead, we use the chain rule to give us a simpler way of working out the answer.What we will do is say u = x2 - 2, meaning that y = u2 we now differentiate y with respect to u, so:dy/du = 2uNext, we want to differentiate u with respect to x, so:du/dx = 2xNow, we can neatly combine the two, as (dy/du) * (du/dx) = dy/dx in the same way that it would with a normal fraction.So, dy/dx = 2u * 2xFinally, we want to have this only in terms of x, so we substitute back in the u equation we established to start with.Giving dy/dx = 4x * (x2 - 2)

Answered by Oliver B. Maths tutor

3055 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A cricket player is capable of throwing a ball at velocity v. Neglecting air resistance, what angle from the horizontal should they throw at to achieve maximum distance before contact with the ground? How far is that distance?


Differentiate e^2x


Find the derivative of the function y = (2x + 12)/(1-x)


A mass of 3kg rests on a rough plane inclined at 60 degrees to the horizontal. The coefficient of friction is 1/5. Find the force P acting parallel to the plane applied to the mass, in order to just prevent motion down the plane.


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