derivative

The _instantaneous_ rate of change of a function at a point — defined as the limit of secant slopes as the interval between the two sample points shrinks to zero: `f'(a) = lim_{h→0} (f(a+h) − f(a)) / h`. The derivative of position is velocity; of velocity, acceleration; of mass-with-respect-to-time, mass flow. Geometrically, the slope of the tangent line. Algebraically, the operation that turns `x²` into `2x` and `sin x` into `cos x`. Almost every quantity called a _rate_ anywhere in physics, ML, and engineering is some derivative.