Double Prime in LaTeX (f''(x))

Where it is used

Second derivative of f at x in prime notation, describing concavity or acceleration.

Two apostrophes in math mode combine into a single superscript with two primes, matching f^{\prime\prime}. The second derivative test uses it: if f'(c) = 0 and f''(c) > 0, then c is a local minimum. In mechanics, x''(t) gives acceleration, though the dot form \ddot{x} is preferred for time derivatives. Three primes f''' are still readable, but beyond that switch to f^{(4)}(x), with the order in parentheses so it is not mistaken for a power. Never type a double quote character in place of two apostrophes; it renders as a different glyph entirely.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Double Prime: $f''(x)$

\[ f''(x) + \omega^2 f(x) = 0 \]
\end{document}

Related symbols

• Dot\dot{x}
• Prime Derivativef'(x)
• Double Dot\ddot{x}
• Differentialdx
• Approaches\to
• Product\prod_{n=1}^{\infty}

Frequently asked questions

How do I write Double Prime in LaTeX?

Type f''(x) in math mode, for example $f''(x) + \omega^2 f(x) = 0$. It works in plain LaTeX without loading any package.

Which package do I need for f''(x)?

None. f''(x) is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use f''(x) in text mode, or only in math mode?

Both. f''(x) compiles in running text as well as inside $...$; in a formula keep it in math mode so it gets math fonts and spacing.