# Math' evaluation notation

Often when you write math longer it become clearer. Consider: we have a function $$ f(x)=foo(x,x_0) $$ and we want to calculate something like $f^{(k)}(x_k)$ where $f^{(k)}$ is the k. derivative of $f$ to $x$

we end up with $$f^{(k)}(x_k) = \underbrace{foo^{(k)}}_\text{derivate}\underbrace{(x_k,x_0)}_\text{apply}$$ the $x$ is gone and i can't deduce easily what was the $x$ without looking for defintion of $foo$.

What we need here is a ability to delay the evaluation and put the actual value later

And there is a notation for this, which is mostly used in one single use-case (evaluation of indefinite integral) but i feel it deserve broader application $$foo^{(x)}(x,x_0)\bigg|_{x=x_k}$$

in Mathematica one write this as `D[foo,{x,k}]/.{x -> x`

(the _{k}}`/.`

part is Mathematica's apply replacement rules operator)

But with my bad handwriting `/.`

looks very indistinguishable and in $\big|_{x=y}$ i mess up the baselines so I eventually overloaded the $@$ operator (once again) and write following: $$\Large\mathbb{e}^{\pi\mskip -7.8 mu \pi \mathbb{i} \frac{x}{p}}\normalsize@(x\mapsto x_0)$$