Symbols:Prime/Derivative

Derivative

$\map {f^\prime} x$

Used to denote the derivative of a function.

Thus for a function $\map f x$:

$\map {f^\prime} x$ denotes the first derivative of $\map f x$

$\map {f^{\prime \prime} } x$ denotes the second derivative of $\map f x$

$\map {f^{\prime \prime \prime} } x$ denotes the third derivative of $\map f x$.

For $n$ beyond $3$, it is usual to use the notation $\map {f^{\paren n} } x$ for the $n$th derivative of $\map f x$.

The $\LaTeX$ code for $\map {f^\prime} x$ is \map {f^\prime} x or \map {f'} x.

The $\LaTeX$ code for $\map {f^{\prime \prime} } x$ is \map {f^{\prime \prime} } x or \map {f' '} x.

The $\LaTeX$ code for $\map {f^{\prime \prime \prime} } x$ is \map {f^{\prime \prime \prime} } x or \map {f' ' '} x.

Note that there are rendering issues with the prime symbol $'$ in the Mathjax version of $\LaTeX$.

Spaces need to be included between adjacent instances of $'$.

Otherwise, MathJax will interpret consecutive instances as compiler imperatives to implement italics or bold.

Hence, for example, the $\LaTeX$ for $x' '$ needs to be written as x' '.