1. “Teach A Level Maths” Vol. 1: AS Core Modules
27: Harder Differentiation - Differentiating with Negative and Rational Indices
© Christine Crisp

2. Module C1 Module C2 Edexcel AQA OCR MEI/OCR
"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

3. The Rule for Differentiation
We have differentiated terms of the form where n is a positive integer.
e.g.
The same rule holds when n is negative or a fraction.

4. e.g. 1
N.B
e.g. 2 Find the gradient function, if
Solution:

5. Exercises
Differentiate the following: 1.
Ans: 2.
Ans:

6. To differentiate a term like we need to change
it to a constant multiplied by the variable.
We use one of the laws of indices:

7. e.g.1 Find the gradient function of
Solution:

8. e.g. 2 Differentiate
Solution:
We don’t start to differentiate until all the terms are in the right form
This answer can be left like this or written as
Only the x has a negative index so the 2 doesn’t move!

9. Exercises
Differentiate the following: 1. 2.

10. Another rule of indices enables us to differentiate expressions containing roots such as

11. e.g. 1 Differentiate
Solution:
Using
This answer can be left like this or:
Using

12. We can leave the answer in either form
e.g. 2 Differentiate
Solution:
We can leave the answer in either form

13. SUMMARY
The rule for differentiating can be used for
using
using

14. Exercises
Differentiate the following: 1.

16. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.
For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

17. e.g. 2 Find the gradient function, if
Solution:
e.g. 1
N.B

18. SUMMARY
The rule for differentiating can be used for
using

19. e.g.1 Find the gradient function of
Solution:

20. Solution:
This answer can be left like this or:
e.g. 2 Differentiate
Using