Differentiation: How to use the chain rule

If y is a function of u, which itself is a function of x, then 

dy/dx=(dy/du) x (du/dx)

Differentiate the outer function and multiply by the derivative of the inner function.  

To illustrate this rule, look at the example below:

y=(2x+3)10

in which y=u10 and u=2x+3

Now,

dy/du=10u9=10(2x+3)9

du/dx=2

The chain rule then gives

dy/dx=(dy/du) x (du/dx) = 10(2x+3)9(2) = 20(2x+3)9

 

NH
Answered by Nicolas H. Maths tutor

4980 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is a derivative and how do we calculate it from first principles?


Solve the differential equation dy/dx = y/x(x + 1) , given that when x = 1, y = 1. Your answer should express y explicitly in terms of x.


What is the equation of the tangent to the circle (x-5)^2+(y-3)^2=9 at the points of intersection of the circle with the line 2x-y-1=0


Use implicit differentiation to find dy/dx of the equation 3y^2 + 2^x + 9xy = sin(y).


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