Revision NotesExam QuestionsPast Papers
ASMathsOCRMaths APureRevision NotesDifferentiationDifferentiationDifferentiating Powers of x

Differentiating Powers of x (OCR AS Maths A): Revision Note

Exam code: H230

Roger B

Author

Roger B

Last updated

OCR Maths A: PureCambridge (CIE) Maths: Pure 1AQA Maths: PureEdexcel Maths: Pure

Differentiating powers of x

How do I differentiate expressions with 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 Tips and Tricks

  • 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
For teachers

Ready to test your students on this topic?

  • Create exam-aligned tests in minutes
  • Differentiate easily with tiered difficulty
  • Trusted for all assessment types
Explore Test Builder
Test Builder in a diagram showing questions being picked from different difficulties and topics, and being downloaded as a shareable format.
Test yourself
Previous:Differentiation from First PrinciplesNext:Gradients, Tangents & Normals
Roger B

Author: Roger B

Expertise: Maths Content Creator

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.