Called a fluxion by Isaac Newton, its most common definition states it is the difference of a function at two values divided by the difference between those values as the difference approaches zero.
The generalization of it named after Enrico Fermi can reduce to a covariant variety of it when the time-like curve on which it operates is geodesic, and its Schwarzian variety is used in chaos theory. The Lagrangian, or convective, variety uses the dot product of the gradient and the velocity of a fluid, and Faá di Bruno's formula gives an equation for the nth one of the composition f(g(t)) [eff of gee of tee]. Called a fluxion by Isaac Newton, its most common definition states it is the difference of a function at two values divided by the difference between those values as the difference approaches zero. For 10 points, name this operation, to which the power rule, chain rule, and quotient rule apply, a procedure which one might use to find the slope of a line tangent to a curve.
The generalization of it named after Enrico Fermi can reduce to a covariant variety of it when the time-like curve on which it operates is geodesic, and its Schwarzian variety is used in chaos theory.
{derivative} [accept {derivation} or {differentiation}; accept {fluxion} before it is read from people who like to give 300 year old terms for things]