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

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Harder Differentiation "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" Module C1 AQAEdexcel OCRMEI/OCR Module C2

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

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

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

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

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

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Harder Differentiation Exercises Differentiate the following: 1. 2.

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

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

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

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Harder Differentiation SUMMARY The rule for differentiating can be used for using

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Harder Differentiation Exercises Differentiate the following: 1.

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Harder Differentiation

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

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Harder Differentiation SUMMARY The rule for differentiating can be used for using

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

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

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