Derivative

Calculus · Formula · Not yet linked from a lesson

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

The instantaneous rate of change: the slope of the line between two points on the curve as they slide together. Every gradient-based method is this quantity, generalised to many variables and computed in bulk.

Symbols

ff
The function being differentiated.
hh
The shrinking gap between the two points.
lim⁡\lim
The value the ratio approaches as h goes to zero.
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