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derivative

The slope of a curve at one exact point, written $f'(x)$ ; the number the curve's secant slopes settle on as the two points forming the secant move together.

Examples

For $f(x)=x^2$ , $f'(x)=2x$ , so $f'(1)=2$ -- the same number the secant slopes 3, 2.1, 2.001 settle on.