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For questions about mathematical notation, i.e. the symbols used to represent mathematical objects and operations.
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If d/dx is an operator, on what does it operate?
The question is: how to properly render
$$\frac{d}{dx}: (x ↦ f(x)) ↦ (x ↦ f'(x)),$$
so as to make the tie-in with $x$ explicit.
Since $x ↦ f(x)$ is synonymous with $(λx)f(x)$, which is $f$, itself, by …