the.com/differentiation
the slope of now, telling you how fast things are changing before they finish changing.
means a mathematical operation that turns a function describing a quantity into one describing its instantaneous rate of change.
from born in the 1660s in a priority fight between newton, who called it fluxions and thought in terms of flowing motion, and leibniz, who called it the differential calculus and gave us the dy/dx notation we still use.
newton vs leibnizboth invented it separately, feuded bitterly for decades
notation survivorleibniz lost the priority war but won the symbols
second derivativeacceleration is just differentiation done twice
undoes integrationthe fundamental theorem links the two operations exactly
for instance
newton's laws — force equals mass times acceleration, itself a second derivative
neural network training — backpropagation is chained differentiation across millions of parameters
marginal cost economics — economists differentiate cost functions to find optimal output