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

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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.

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

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

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:

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

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!

Exercises Differentiate the following: 1. 2.

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

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

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

SUMMARY The rule for differentiating can be used for using using

Exercises Differentiate the following: 1.

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

SUMMARY The rule for differentiating can be used for using

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

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