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Diffstat (limited to 'main.tex')
| -rw-r--r-- | main.tex | 2 |
1 files changed, 1 insertions, 1 deletions
@@ -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 |