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**“Teach A Level Maths” Vol. 1: AS Core Modules**

27: Harder Differentiation - Differentiating with Negative and Rational Indices © Christine Crisp

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**Module C1 Module C2 Edexcel AQA OCR MEI/OCR**

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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.

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

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

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**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:

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**e.g.1 Find the gradient function of**

Solution:

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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!

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Exercises Differentiate the following: 1. 2.

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

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

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**We can leave the answer in either form**

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

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SUMMARY The rule for differentiating can be used for using using

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Exercises Differentiate the following: 1.

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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.

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**e.g. 2 Find the gradient function, if**

Solution: e.g. 1 N.B

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SUMMARY The rule for differentiating can be used for using

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**e.g.1 Find the gradient function of**

Solution:

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

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20: Stretches © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules.

20: Stretches © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules.

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