= Weak derivative boundary layer
{title2=$y_{\mathrm{layer}}=O(\delta),\quad y'_{\mathrm{layer}}=O(1)$}
A correction of amplitude $O(\delta)$ varying on width $O(\delta)$ can be negligible in a function's leading outer approximation while producing an order-one change in its derivative. For example $-\delta e^{-x/\delta}$ has derivative $e^{-x/\delta}$, allowing an endpoint derivative condition to be met without changing the leading outer boundary value. Such weak layers matter in <matched asymptotic expansions> involving derivative boundary conditions, even when only another endpoint has an order-one layer in the function itself.
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