Reverse Chain Rule (Edexcel IAL Maths)

Spec point — 5.2

Reverse chain rule

What is the chain rule?

• The Chain Rule is a way of differentiating two (or more) functions

• In many simple cases the above formula/substitution is not needed

• The same can apply for the reverse – integration

How do I integrate using the reverse chain rule?

• In more awkward cases it can help to write the numbers in before integrating

• STEP 1: Spot the ‘main’ function

• STEP 2: ‘Adjust’ and ‘compensate’ any numbers/constants required in the integral

• STEP 3: Integrate and simplify

Exam Hint

• If in doubt you can always use a substitution.
• Differentiation is easier than integration so if stuck try the opposite, eg. sin and cos are linked (remember that minus!) so if integrating a sin function, start by differentiating the corresponding cos function.
• Lastly, check your final answer by differentiating it.

Worked Example