Definition:Derivative/Higher Derivatives/Third Derivative/Notation/Leibniz Notation

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Leibniz's Notation for Third Derivative

Leibniz's notation for the third derivative of a function $y = f \left({x}\right)$ with respect to the independent variable $x$ is:

$\dfrac {\mathrm d^3 y} {\mathrm d x^3}$

Historical Note

Leibniz's notation for a derivative came at about the same time that the manuscript dated $29$th October $1675$ in which the notation for the integral had been devised.

At the same time he introduced the differential symbol $\mathrm d$.

Thus he was soon writing $\mathrm d x$, $\mathrm d y$, and $\dfrac {\mathrm d y} {\mathrm d x}$ soon followed.

In his $1684$ article Nova Methodus pro Maximis et Minimis, published in Acta Eruditorum, he casually drops the notation in place with very little explanation.