When you open Maple, prime notation represents differentiation. So, when you input $A\'$ it means the derivative of $A\left(x\right)$ with respect to $x$. It is a handy shortcut to typing $\mathrm{diff}\left(A\left(x\right)\,x\right)$. This meaning of prime notation as differentiation is the __useprime setting of the Typesetting package__.

There is also another frequent meaning, not differentiation, for prime notation: __primed variables__, typically used when relating variables in different coordinate systems, e.g. $x$ and $x\'$ in two reference systems K and K', or variables that are related in some way (e.g. when working with Green functions), set complement, the dual of a vector space, etc.. New in Maple 2023, by entering $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{useprime}\=\mathrm{false}\right)$, instead of receiving an error message when you input - say - $x\'$, you can now work with $x\'$ as a primed variable. Also new, when you load the __Physics__ package, where transformation of coordinates are the most frequent use of the prime notation, the Typesetting $\mathrm{useprime}$ keyword is automatically set to $\mathrm{false}\.$

For example, this is the default behavior

$A\'$

$\frac{{\ⅆ}}{{\ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{A}{}\left({x}\right)$
| (6.1) |

New: you can work with primed variables

$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{useprime}=\mathrm{false}\right)$

$A\'$

${\mathrm{A\text{'}}}$
| (6.3) |

Turn again ON prime notation to represent differentiation

$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{useprime}\=\mathrm{true}\right)\:$

$A\'$

$\frac{{\ⅆ}}{{\ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{A}{}\left({x}\right)$
| (6.4) |

Load the Physics package or its Physics:-Vectors subpackage

$\mathrm{with}\left(\mathrm{Physics}\right)\:$

$A\'$

${\mathrm{A\text{'}}}$
| (6.5) |

Query about the status of the $\mathrm{useprime}$ setting

$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{useprime}\right)$

You can also change this status directly from the $\mathrm{Physics}:-\mathrm{Setup}$ command using a keyword complementary to the one of $\mathrm{Typesetting}$; query, then change it

$\mathrm{Setup}\left(\mathrm{prime}\right)$

$\left[{\mathrm{primedvariables}}{=}{\mathrm{true}}\right]$
| (6.7) |

$\mathrm{Setup}\left(\mathrm{primedvariables}equals;\mathrm{false}\right)$

$\left[{\mathrm{primedvariables}}{=}{\mathrm{false}}\right]$
| (6.8) |

$A\'$

$\frac{{\ⅆ}}{{\ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{A}{}\left({x}\right)$
| (6.9) |

${}$