← Calculus Studio

Chapter 4

Rules from pictures

A growing square, a growing rectangle, two gears: the rules of differentiation, seen first.

1

A square that grows

A square of side x = 3 grows by a little dx. It gains two strips and a small white corner. Shrink dx.

x²x = 3dxtwo strips: 2 · 3 · 0.8 = 4.8corner: 0.8² = 0.64growth ÷ dx = 6.8

Drag the slider right: dx gets smaller, and the corner shrinks much faster than the strips.

Next chapter: Reading the shape →