differentiation from first principles
What differentiation from first principles means in Mathematics A-Level, as defined for Pearson Edexcel, WJEC.
Definitions of differentiation from first principles
Exam boards and our study guides word this term in slightly different ways. Learn the version your board uses.
Check what you remember
Read the wording for your board, then hide it and explain differentiation from first principles in your own words. Rough notes are fine. This is a self-check, with no mark or grade.
Reference: Pearson Edexcel
Taking the limit of [f(x + h) − f(x)] ÷ h as h tends to zero, for small positive integer powers of x and for sin x and cos x.
Establishes derivative formulas directly from the formal limit definition for small positive integer powers of x.
The formal definition gives f'(x) = lim_(h→0) [f(x + h) − f(x)] / h, used for sin x and cos x.
Topics that use differentiation from first principles
- Differentiation (Pearson Edexcel A-Level)
- Differentiation (A2 Unit 3: Pure Mathematics B) (WJEC A-Level)
- Differentiation (AS Unit 1: Pure Mathematics A) (WJEC A-Level)
Related terms
- second derivative
- Chain rule
- connected rates of change
- Derivative
- Implicit differentiation
- Parametric differentiation
- Product rule
- Quotient rule
Using differentiation from first principles in the exam
Check the command word and mark scheme for your exact question. After comparing your explanation with the reference, use the term in an answer on the linked topic. This practice does not predict an exam mark.
Practise Mathematics questions
Create a free account to answer exam-style questions on this topic and get feedback on your answers.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge