How do I differentiate expressions involving powers of x?
- Powers of x are differentiated according to the following formulae:
- Differentiating terms with positive integer powers of x is straightforward
- But negative and fractional powers of x can also be differentiated this way
- Don't forget these two special cases:
- These allow you to differentiate constants and linear terms in x
- If the expression involves a sum or difference of terms just differentiate one term at a time
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
