Calculus
Advanced

Derivative (Limit Definition)

Formal definition of the derivative.

Formula

f′(x)=lim⁡h→0f(x+h)−f(x)hf'(x) = \lim_{h \to 0}\frac{f(x+h)-f(x)}{h}

Variables

fFunction
hSmall increment

Example

For f(x) = x²: f′(x) = lim (x+h)²−x²)/h = lim (2x + h) = 2x.

Did You Know?

This limit is the rigorous definition of a derivative — the slope of a line touching a curve at a single point.

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