Mr. Integral
Math notes/Calculus I/The Derivative

The Derivative from First Principles — Cheat sheet

CHEAT SHEET   ·   FREE

Choose “Save as PDF” in the print dialog.
On this page

Core rule

f′(a)=lim⁡h→0f(a+h)−f(a)h.f'(a)=\lim_{h\to0}\frac{f(a+h)-f(a)}h.

Tangent line: y=f(a)+f′(a)(x−a)y=f(a)+f'(a)(x-a). Derivative units are output units divided by input units.

Watch for

A jump, corner or infinite slope can prevent a finite derivative. A finite secant slope is an approximation, not the limit itself.