linguistic:paraphrasing, stylistic:style_transfer
Notation

The second derivative of a function f (x) {\displaystyle f(x)} is usually denoted f ″ (x) {\displaystyle f''(x)}. That is: f ″ = (f ′) ′ {\displaystyle f''=\left(f'\right)'} When using Leibniz's notation for derivatives, the second derivative of a dependent variable y with respect to an independent variable x is written d 2 y d x 2. {\displaystyle {\frac {d^{2}y}{dx^{2}}}.} This notation is derived from the following formula: d 2 y d x 2 = d d x (d y d x). {\displaystyle {\frac {d^{2}y}{dx^{2}}}\,=\,{\frac {d}{dx}}\left({\frac {dy}{dx}}\right).}