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authorJaron Kent-Dobias <jaron@kent-dobias.com>2019-08-23 17:02:38 -0400
committerJaron Kent-Dobias <jaron@kent-dobias.com>2019-08-23 17:02:38 -0400
commit3e1c9cfa3dc9aabcf66fb8f93ccdf816ee4459f7 (patch)
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parentc94d723e095fc34137bc50efe41a082949f926fd (diff)
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functionalfunctional functional
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diff --git a/main.tex b/main.tex
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@@ -314,7 +314,7 @@ cannot be solved explicitly, we can make use of the inverse function theorem.
First, denote by $\eta^{-1}[\eta]$ the inverse functional of $\eta$ implied by
\eqref{eq:implicit.eta}, which gives the function $\epsilon_\X$ corresponding
to each solution of \eqref{eq:implicit.eta} it receives. Now, we use the inverse function
-theorem to relate the functional reciprocal of the functional derivative of $\eta[\epsilon]$ with respect to $\epsilon_\X$ to the functional derivative of $\eta^{-1}[\eta]$ with respect to $\eta$, yielding
+theorem to relate the functional reciprocal of the derivative of $\eta[\epsilon]$ with respect to $\epsilon_\X$ to the derivative of $\eta^{-1}[\eta]$ with respect to $\eta$, yielding
\begin{equation}
\begin{aligned}
\bigg(\frac{\delta\eta(x)}{\delta\epsilon_\X(x')}\bigg)^\recip