1. Negative and Rational Indices all slides © Christine Crisp
3.6 Differentiation
AS 91578
Negative and Rational Indices
all slides © Christine Crisp

2. 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.

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

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

5. 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:

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

7. 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!

8. Exercises
Differentiate the following: 1. 2.

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

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

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

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

13. Exercises
Differentiate the following: 1.