Sulba
000 / 100

Calculus · from the very first idea

Calculus,from the first idea.

What a slope is, how a curve has one at every point, and how to find it — each step drawn and derived by hand, then checked by measuring, then put to work on exam questions.

Start with Derivatives, from first principlesYour progress
f′(x) = 2x5 steps, derived by hand4 curves to drag
Lessons in Module 1
9
Steps in the first
5
Curves to drag
4
Exam question
1
0/1

Your progress

Open any lesson to begin, and mark it understood when the idea clicks.

The course

Derivatives, from first principles

Five steps from “a function is a rule” to f′(x) = 2x, derived by hand and then checked against a measurement.

Calculus · lesson

  1. 01A function is a rule.
  2. 02Steepness is rise over run.
  3. 03Bring the two points together.
  4. 04Now do it with algebra, once.
  5. 05Check it. Then look at what the slopes make.
Start the lesson

Module 1 · the lessons

  1. 01SteepnessComing
  2. 02Curves don't have one steepnessComing
  3. 03Zoom in far enough and a curve is straightComing
  4. 04The tangent lineComing
  5. 05Secant into tangentComing
  6. 06The derivative is its own curveComing
  7. 07Reading the signsComing
  8. 08The power ruleComing
  9. 09Position becomes velocityComing

01 · Exam questions

Exam questions

Questions set the way an exam paper sets them, solved from the beginning in sixty seconds, every line of the working shown.

EXAM QUESTION 01 · MODULE 1 · DERIVATIVES

From first principles

The curve C has equation

y = x² + 3x.

(a) Prove, from first principles,

that dy/dx = 2x + 3.

(b) Find the gradient of C

at the point P(2, 10).

(c) Find an equation of the

tangent to C at P.

Watch it solved