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The math you are already using.

A cooling coffee, a loan statement, the slope of a curve: each one runs on a formula you can write down and check. These pages show the formula, the steps and where it came from.

Start with a normal dayDerivative rules cheat sheet

Slide the dot along the coffee's curve

A cooling coffee drawn as a curve with a sliding tangent lineTemperature falls steeply at first and then flattens. The tangent line at the dot slopes sharply down near the start and is almost level near the end, so the rate of cooling shrinks as the coffee nears room temperature.room temperaturetimetemperature

Steep: the coffee is cooling fast.

The slope of the curve at any moment is a derivative: how fast the coffee is cooling right now. The curve is a sketch, not measured data.

Pick a corner of everyday math

Why you can check our work

30pages published, each ending in a numbered list of its sources
221distinct sources: 93 textbooks, course notes and journals, 80 government pages, 48 others
October 21, 2026most recent check. Every page shows its own date
Explanations onlyNo advice on money or health. How pages are checked

Looking at a loan?

The payment formula, step by step, with a worked example and a calculator you can redo.

See the formula