Differentiation Rules

Chain Rule

Where is it used?

The chain rule is used where the required for differentiation of equations that have layers to them. For example, finding dy/dx in y=f(u), where u=g(x).


What is the Formula?

Where g(u) is the first layer and f(x) is the second layer and the required differentiation that needs to be found is dy/dx.


The chain rule works with an infinite number of layers. Of course, the more layers there are the more difficult it becomes. For example, the formula for the chain rule for four layers would be.

Step 2: Substitute  g'(u) and f'(x) into the chain rule formula.

Test Your Knowledge!
Test Style Chain Rule Questions

Download a free worksheet containing 5 chain rule questions with worked solutions and allocated marks for each question.

To Download, Click on Your Desired Format:

Step 3: Substitute other variables until there is only one variable. In this example, we will substitute u with 2x^2+5x so the equation only has one variable.

Step 4: Expand and then Simplify the equation.

Worked Example

In this example, we will differentiate (dy/dx) y=5u^2+6u+3, u=2x^2+5x


Step 1: Determine the equations g'(x), f(x)

Email: christian.bien@atarsurvivalguide.com

ABN: 87 574 760 103

  • Facebook - Black Circle
  • YouTube - Black Circle

"ATAR" is a registered trademark of Monash University as a Trustee For The Victorian Tertiary Admission Centre .The School Curriculum and Standards Authority (SCSA) have no involvement in or responsibility for any material appearing on this site. Nor does SCSA endorse or make any warranties regarding the study resources, current and past WACE exams available on this site or sold by Christian Bien. 

Copyright © 2020 Christian Bien at the ATAR Survival Guide