Differentiating Powers of x (Edexcel AS Maths): Revision Note
Did this video help you?
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](https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=3840/https://cdn.savemyexams.com/uploads/2020/07/7.1.3-Pwrs-of-x-Illustr-1.png)
Differentiating terms with positive integer powers of x is straightforward
![Pwrs of x Illustr 2, A Level & AS Maths: Pure revision notes](https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=3840/https://cdn.savemyexams.com/uploads/2020/07/7.1.3-Pwrs-of-x-Illustr-2.png)
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](https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=3840/https://cdn.savemyexams.com/uploads/2020/07/7.1.3-Pwrs-of-x-Illustr-3.png)
Don't forget these two special cases:
![Pwrs of x Illustr 4, A Level & AS Maths: Pure revision notes](https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=3840/https://cdn.savemyexams.com/uploads/2020/07/7.1.3-Pwrs-of-x-Illustr-4.png)
These allow you to differentiate constants and linear terms in x
![Pwrs of x Illustr 4b, A Level & AS Maths: Pure revision notes](https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=3840/https://cdn.savemyexams.com/uploads/2020/07/7.1.3-Pwrs-of-x-Illustr-4b.png)
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](https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=3840/https://cdn.savemyexams.com/uploads/2020/07/7.1.3-Pwrs-of-x-Illustr-5.png)
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](https://cdn.savemyexams.com/cdn-cgi/image/f=auto,width=3840/https://cdn.savemyexams.com/uploads/2020/07/7.1.3-Pwrs-of-x-Example.png)
You've read 0 of your 5 free revision notes this week
Sign up now. It’s free!
Did this page help you?