Symbols:Prime/Usage

Various Usages of the Prime Symbol

The prime symbol ${}^\prime$ can be used in the following ways:

Feet and Inches

${}^\prime$ and ${}^{\prime \prime}$

One of the symbols in general use for feet and inches is ${}^{\prime}$ and ${}^{\prime \prime}$.

Thus, for example, $6$ feet $3$ inches is presented as:

$6^\prime \, 3^{\prime \prime}$

The $\LaTeX$ code for \(6^\prime \, 3^{\prime \prime}\) is 6^\prime \, 3^{\prime \prime}  or 6' \, 3' '.

Minutes and Seconds

${}^\prime$ and ${}^{\prime \prime}$

The usual symbols in general use for minutes and seconds are ${}^{\prime}$ and ${}^{\prime \prime}$.

Thus, for example, an angle of $10$ degrees, $3$ minutes and $27$ seconds is presented as:

$10 \degrees \, 3^\prime \, 27^{\prime \prime}$

The $\LaTeX$ code for \(10 \degrees \, 3^\prime \, 27^{\prime \prime}\) is 10 \degrees \, 3^\prime \, 27^{\prime \prime}  or 10 \degrees \, 3' \, 27^' '.

Inch

${}^{\prime \prime}$

One of the symbols in general use for the inch is ${}^{\prime \prime}$.

Thus, for example, $10$ inches is presented as:

$10^{\prime \prime}$

The $\LaTeX$ code for \(10^{\prime \prime}\) is 10^{\prime \prime}  or 10' '.

Second

${}^{\prime \prime}$

The usual symbol in general use for the second is ${}^{\prime \prime}$.

Thus, for example, $27$ seconds is presented as:

$27^{\prime \prime}$

The $\LaTeX$ code for \(27^{\prime \prime}\) is 27^{\prime \prime}  or 27' '.

Constant Value of Variable

$\tuple {x^\prime, y^\prime}$

Often used to represent a constant value of a variable.

For example, let $\tuple {x, y}$ denote the Cartesian coordinates of a variable point in the plane describing the locus of a curve.

Then $\tuple {x', y'}$ can be used to denote an arbitrary constant point on that curve.

The $\LaTeX$ code for \(\tuple {x^\prime, y^\prime}\) is \tuple {x^\prime, y^\prime}  or \tuple {x', y'}.

Related Variable

$\tuple {x^\prime, y^\prime}$

Often used to represent a variable or constant which is related in some way to another previously declared variable or constant.

For example, let $\tuple {x, y}$ denote the Cartesian coordinates of a variable point in the plane.

Then $\tuple {x', y'}$ can be used to denote the same point in the plane after a transformation.

The $\LaTeX$ code for \(\tuple {x^\prime, y^\prime}\) is \tuple {x^\prime, y^\prime}  or \tuple {x', y'}.

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.

Technical Note

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' '.