AQA A Level Maths: Pure复习笔记7.1.3 Differentiating Powers of x

Differentiating Powers of x

How do I differentiate expressions involving powers of x?

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

7.1.3-Pwrs-of-x-Illustr-1

  • Differentiating terms with positive integer powers of x is straightforward

7.1.3-Pwrs-of-x-Illustr-2

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

7.1.3-Pwrs-of-x-Illustr-3

  • Don't forget these two special cases:

7.1.3-Pwrs-of-x-Illustr-4

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

7.1.3-Pwrs-of-x-Illustr-4b

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

7.1.3-Pwrs-of-x-Illustr-5

Exam 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

7.1.3-Pwrs-of-x-Example

 

 

 

 

 

 

转载自savemyexams

更多Alevel课程
翰林国际教育资讯二维码