Fluxion (mathematics)

The fluxion of a "fluent" (a time-varying quantity, or function) is its instantaneous rate of change, or gradient, at a given point. Fluxions were introduced by Isaac Newton to describe his form of a derivative with respect to time. Newton introduced the concept in 1665 and detailed them his mathematical treatise, Method of Fluxions. Fluxions and fluents made up Newton's early calculus.

Fluxions were central to the Leibniz–Newton calculus controversy, when Newton sent a letter to Gottfried Wilhelm Leibniz explaining them, but concealing his words in code due to his suspicion. He wrote:

I cannot proceed with the explanations of the fluxions now, I have preferred to conceal it thus: 6accdæ13eff7i319n4o4qrr4s8t12vz

The gibberish string was in fact an enciphered Latin phrase, meaning: "Given an equation that consists of any number of flowing quantities, to find the fluxions: and vice versa".

If the fluent ${\displaystyle y}$ is defined as ${\displaystyle y=t^{2}}$ (where ${\displaystyle t}$ is time) the fluxion (derivative) at ${\displaystyle t=2}$ is:

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