Subjects / LC Mathematics / Functions and Calculus

Differentiation from first principles

Use the limit definition of the derivative to differentiate simple functions.

5th Year6th Year Higher

15practice questions

Match the pairs: 1 · Multiple choice: 6 · Numeric answer: 3 · Put in order: 2 · Short answer: 1 · Written answer (self/teacher assessed): 2

Each question has up to three hints, a worked explanation, and is tracked in your progress and review plan.

Try a question

Put in orderPaper 1 – Functions and Calculus

Put the steps for differentiating f(x) from first principles in order.

Give each item its position (1 = first).

Take the limit as h → 0

Write down f(x + h)

Divide by h

Find f(x + h) − f(x) and simplify

Hint 1

The definition is f′(x) = lim (h→0) [f(x + h) − f(x)]/h.

Create a free account to save your progress.