Leibniz's notation

In calculus [Calculus], Leibniz’s notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz [Gottfried Leibniz], uses the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y, respectively, just as Δx and Δy represent finite increments of x and y, respectively.

Consider y as a function of a variable x, or y = f(x). If this is the case, then the derivative of y with respect to x, which later came to be viewed as the limit

\(\displaystyle \lim _{\Delta x\rightarrow 0}{\frac {\Delta y}{\Delta x}}=\lim _{\Delta x\rightarrow 0}{\frac {f(x+\Delta x)-f(x)}{\Delta x}\)

was, according to Leibniz, the quotient of an infinitesimal increment of y by an infinitesimal increment of x, or

\(\displaystyle {\frac {dy}{dx}}=f’(x)}\)

(“Leibniz’s Notation” 2022)

Bibliography

Backlinks

• Chain rule
• Product rule
• Silvanus Thompson | Calculus Made Easy