Notation For Differentiation - Lagrange's Notation

Lagrange's Notation

One of the most common modern notations for differentiation is due to Joseph Louis Lagrange and uses the prime mark: the first three derivatives of f are denoted

for the first derivative,

for the second derivative,

for the third derivative.

After this, some authors continue by employing Roman numerals such as f IV for the fourth derivative of f, while others put the number of derivatives in brackets, so that the fourth derivative of f would be denoted f (4). The latter notation extends readily to any number of derivatives, so that the nth derivative of f is denoted f (n).