MathsYears 12–13Differentiation

Differentiation from first principles

Derive the derivative as a limit of (f(x+h)-f(x))/h; differentiate x^n, sin x, cos x, e^x, ln x

What you'll learn

  1. 1

    Imagine driving along a curvy road. Your speedometer shows your speed at each exact moment — that's the derivative!

  2. 2

    What does the derivative tell you at a point on a curve?

  3. 3

    Let's find the derivative of f(x) = x² from first principles.

  4. 4

    Drag the point along the curve to see the slope change as h gets smaller.

  5. 5

    In the formula for first principles, what do we do to h at the end?

  6. 6

    Using first principles, what is the derivative of f(x) = x²?

  7. 7

    Which step comes first in first principles?

Practise Differentiation from first principles with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.

Start free →Sign in