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What does the notation "$|_{\epsilon=0}$" at the bottom of the derivative mean?

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It (probably) means you evaluate that derivative in $\epsilon = 0$.

For example, if $f(x) = x^2$, then: $$\frac{df}{dx}\Bigr|_{x=3} = 2x\Bigr|_{x=3} = 6$$

See also: What is the name of the vertical bar?

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