Differentiating Powers of x (AQA A Level Maths: Pure)

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Differentiating Powers of x

How do I differentiate expressions involving powers of x?

  • Powers of x are differentiated according to the following formulae:

Pwrs of x Illustr 1, A Level & AS Maths: Pure revision notes

  • Differentiating terms with positive integer powers of x is straightforward

Pwrs of x Illustr 2, A Level & AS Maths: Pure revision notes

  • But negative and fractional powers of x can also be differentiated this way

Pwrs of x Illustr 3, A Level & AS Maths: Pure revision notes

 

  • Don't forget these two special cases:

 Pwrs of x Illustr 4, A Level & AS Maths: Pure revision notes

  • These allow you to differentiate constants and linear terms in x

Pwrs of x Illustr 4b, A Level & AS Maths: Pure revision notes

  • If the expression involves a sum or difference of terms just differentiate one term at a time

 

Pwrs of x Illustr 5, A Level & AS Maths: Pure revision notes

Examiner Tip

  • Take extra care when differentiating negative and fractional powers of x as mishandling negative signs and fractions is a common way to lose marks in these sorts of questions.

Worked example

Pwrs of x Example, A Level & AS Maths: Pure revision notes

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Roger

Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.