documentclass{article}
usepackage{cancel}
usepackage{tikz}
usetikzlibrary{calc,positioning,tikzmark}
tikzset{CancelTo/.is family,
CancelTo,
angle/.initial=60,
name/.initial=tmp,
node/.style={},
arrow/.style={->},
topoffs/.initial=2pt,
nodeaboveoffs/.initial=1pt,
nodeleftoffs/.initial=0pt
}
newcommand{CancelTo}[3][]{bgrouptikzset{CancelTo/.cd,#1}
tikzmarknode{pgfkeysvalueof{/tikz/CancelTo/name}}{#3}
begin{tikzpicture}[overlay,remember picture]
  draw[/tikz/CancelTo/arrow] let p1=($(pgfkeysvalueof{/tikz/CancelTo/name}.north)-(pgfkeysvalueof{/tikz/CancelTo/name}.south)$),n1={0.5*y1*cot(pgfkeysvalueof{/tikz/CancelTo/angle})},n2={y1/sin(pgfkeysvalueof{/tikz/CancelTo/angle})}
  in ([xshift=-n1]pgfkeysvalueof{/tikz/CancelTo/name}.south) -- ++ (pgfkeysvalueof{/tikz/CancelTo/angle}:n2+pgfkeysvalueof{/tikz/CancelTo/topoffs})
  node[above left=pgfkeysvalueof{/tikz/CancelTo/nodeaboveoffs} and pgfkeysvalueof{/tikz/CancelTo/nodeleftoffs},inner sep=0pt,font=scriptsize,/tikz/CancelTo/node] (tmplabel) {#2};
  path let p1=($(tmplabel.north east)-(pgfkeysvalueof{/tikz/CancelTo/name}.east)$) in
  pgfextra{xdefmydist{x1}};
end{tikzpicture}egroupvphantom{cancelto{#2}{#3}}hspace{mydist}}
newcommand{pd}[2]{frac{partial #1}{partial #2}}
begin{document}
textbf{Problem 1 (``narrow" term):}
With zero offset:
begin{equation}
  CancelTo[nodeleftoffs=0pt]{ignore}{pd{f}{x}} +
  pd{g}{y} = 0
end{equation}
With offset of $-11$pt:
begin{equation}
  CancelTo[nodeleftoffs=-11pt]{ignore}{pd{f}{x}} +
  pd{g}{y} = 0
end{equation}
What I would like to get (spacing between first fraction and $+$ unaffected):
begin{equation}
  CancelTo[nodeleftoffs=-11pt]{ignore}{pd{f}{x}} !!!!!! +
  pd{g}{y} = 0
end{equation}
textbf{Problem 2 (``wide" term):}
Equation without arrow:
begin{equation}
  (a+b)pd{f}{x} + pd{g}{y} = 0
end{equation}
Equation with arrow and zero offset:
begin{equation}
  CancelTo[nodeleftoffs=0pt]{ignore}{(a+b)pd{f}{x}} +
  pd{g}{y} = 0
end{equation}
What I would like to get (spacing between first fraction and $+$ unaffected):
begin{equation}
  CancelTo[nodeleftoffs=-11pt]{ignore}{(a+b)pd{f}{x}} ;, +
  pd{g}{y} = 0
end{equation}
end{document}