It is assuming that $x$ and $y$ are independent variables and as you're differentiating with respect to $y$, that term vanishes since it doesn't contain any $y$'s
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Variable $x$ is treated like a constant (becouse you are differentiating with respect to $y$). So $$(-e^x)'=(-e^C)'=(C)'=0.$$
It is assuming that $x$ and $y$ are independent variables and as you're differentiating with respect to $y$, that term vanishes since it doesn't contain any $y$'s