${{ r} ^I} = {\overset{I\downarrow}{\left[\begin{matrix} h \\ x\end{matrix}\right]}}$
${{{ e} _u} ^I} = {\overset{u\downarrow I\rightarrow}{\left[\begin{array}{cc} 1& 0\\ \frac{\partial h}{\partial x}& 1\end{array}\right]}}$
${{{ \eta} _I} _J} = {\overset{I\downarrow J\rightarrow}{\left[\begin{array}{cc} -1& 0\\ 0& 1\end{array}\right]}}$
${{{ g} _u} _v} = {\overset{u\downarrow v\rightarrow}{\left[\begin{array}{cc} -{1}& -{\frac{\partial h}{\partial x}}\\ -{\frac{\partial h}{\partial x}}& {1}{-{{\frac{\partial h}{\partial x}}^{2}}}\end{array}\right]}}$
zero skew components:
${{{ g} _u} _v} = {\overset{u\downarrow v\rightarrow}{\left[\begin{array}{cc} -{1}& 0\\ 0& {1}{-{{\frac{\partial h}{\partial x}}^{2}}}\end{array}\right]}}$
set metric
${{{ g} ^u} ^v} = {\overset{u\downarrow v\rightarrow}{\left[\begin{array}{cc} \frac{{1}{-{{\frac{\partial h}{\partial x}}^{2}}}}{{-{1}} + {{\frac{\partial h}{\partial x}}^{2}}}& 0\\ 0& \frac{1}{{1}{-{{\frac{\partial h}{\partial x}}^{2}}}}\end{array}\right]}}$
${{ n} ^u} = {\overset{u\downarrow}{\left[\begin{matrix} {n^t} \\ {n^x}\end{matrix}\right]}}$
${{ n} _I} = {{\overset{I\downarrow}{\left[\begin{matrix} {{n^t}} + {{{{n^x}}} \cdot {{\frac{\partial h}{\partial x}}}} \\ {n^x}\end{matrix}\right]}} = {\overset{I\downarrow}{\left[\begin{matrix} 0 \\ 0\end{matrix}\right]}}}$
${ n} ^t$ from ${ n} ^x$ : ${{n^t}} = {-{{{{n^x}}} \cdot {{\frac{\partial h}{\partial x}}}}}$
$n \cdot n = -1$ : ${{-{{{n^t}}^{2}}} + {{{n^x}}^{2}}{-{{{{{n^x}}^{2}}} {{{\frac{\partial h}{\partial x}}^{2}}}}}} = {-1}$
${{{{n^x}}^{2}}{-{{{2}} {{{{n^x}}^{2}}} {{{\frac{\partial h}{\partial x}}^{2}}}}}} = {-{1}}$
$n^x$ solutions:
${{n^x}} = {-{{{i}} {{\frac{1}{\sqrt{{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}}}}}$
${{n^x}} = {{{i}} {{\frac{1}{\sqrt{{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}}}}$
solving the first one first (keep note that they're plus or minus...)
${ n} ^x$ is $-{{{i}} {{\frac{1}{\sqrt{{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}}}}$
should be $\frac{ {-{\frac{\partial h}{\partial x}}} {{\sqrt{{4} + {{{8}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{12}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}}}{{-2}{-{{{4}} {{{\frac{\partial h}{\partial x}}^{4}}}}} + {{{6}} {{{\frac{\partial h}{\partial x}}^{2}}}}}$
rewritten by hand : ${{n^x}} = {\frac{\frac{\partial h}{\partial x}}{\sqrt{{{\left({{1}{-{{\frac{\partial h}{\partial x}}^{2}}}}\right)}} {{\left({{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}}}}}$
$n^t$ solutions:
${{n^t}} = {-{\frac{{\frac{\partial h}{\partial x}}^{2}}{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}}}$
${{n^t}} = {\frac{{\frac{\partial h}{\partial x}}^{2}}{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}}$
should be $\frac{{-1} + {{\frac{\partial h}{\partial x}}^{2}}}{-{\sqrt{{1}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}}}}$
${{n^t}} = {\sqrt{\frac{{1}{-{{\frac{\partial h}{\partial x}}^{2}}}}{{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}}$
${{ n} ^u} = {\overset{u\downarrow}{\left[\begin{matrix} \frac{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}{{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}} \\ \frac{\frac{\partial h}{\partial x}}{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}\end{matrix}\right]}}$
$n_\hat{x} = 0$
${\overset{I\downarrow}{\left[\begin{matrix} \frac{1}{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}} \\ \frac{\frac{\partial h}{\partial x}}{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}\end{matrix}\right]}} = {0}$
n dot n = -1
${\frac{{-{1}} + {{{7}} {{{\frac{\partial h}{\partial x}}^{2}}}}{-{{{8}} {{{\frac{\partial h}{\partial x}}^{8}}}}}{-{{{18}} {{{\frac{\partial h}{\partial x}}^{4}}}}} + {{{20}} {{{\frac{\partial h}{\partial x}}^{6}}}}}{{1}{-{{{7}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{8}} {{{\frac{\partial h}{\partial x}}^{8}}}} + {{{18}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{20}} {{{\frac{\partial h}{\partial x}}^{6}}}}}}} = {-1}$
1st kind Christoffel
${{{{ \Gamma} _a} _b} _c} = {\overset{a\downarrow[{b\downarrow c\rightarrow}]}{\left[\begin{matrix} \overset{b\downarrow c\rightarrow}{\left[\begin{array}{cc} 0& 0\\ 0& 0\end{array}\right]} \\ \overset{b\downarrow c\rightarrow}{\left[\begin{array}{cc} 0& 0\\ 0& -{{{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\frac{\partial h}{\partial x}}}}\end{array}\right]}\end{matrix}\right]}}$

2nd kind Christoffel
${{{{ \Gamma} ^a} _b} _c} = {\overset{a\downarrow[{b\downarrow c\rightarrow}]}{\left[\begin{matrix} \left[\begin{array}{cc} 0& 0\\ 0& 0\end{array}\right] \\ \left[\begin{array}{cc} 0& 0\\ 0& -{\frac{{{\frac{\partial h}{\partial x}}} {{\frac{\partial^ 2 h}{\partial x^ 2}}}}{{1}{-{{\frac{\partial h}{\partial x}}^{2}}}}}\end{array}\right]\end{matrix}\right]}}$

${{ n} _u} = {\overset{u\downarrow}{\left[\begin{matrix} -{\frac{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}{{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}} \\ \frac{{{\frac{\partial h}{\partial x}}} {{\left({{1}{-{{\frac{\partial h}{\partial x}}^{2}}}}\right)}}}{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}\end{matrix}\right]}}$
$\partial_u n_v = $$\overset{u\downarrow v\rightarrow}{\left[\begin{array}{cc} 0& \frac{{{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\left({{-{1}} + {{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}\right)}} {{\frac{\partial h}{\partial x}}}}{{{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{4}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{4}} {{{\frac{\partial h}{\partial x}}^{4}}}}}\right)}}}\\ 0& \frac{{{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\left({{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{6}}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{4}} {{{\frac{\partial h}{\partial x}}^{4}}}}}\right)}}}{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}}}\end{array}\right]}$
$\nabla_u n_v = $$\overset{u\downarrow v\rightarrow}{\left[\begin{array}{cc} 0& \frac{{{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\left({{-{1}} + {{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}\right)}} {{\frac{\partial h}{\partial x}}}}{{{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{4}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{4}} {{{\frac{\partial h}{\partial x}}^{4}}}}}\right)}}}\\ 0& \frac{{{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\left({{1} + {{\frac{\partial h}{\partial x}}^{4}}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}}}{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}}}\end{array}\right]}$
${{\perp} = {{{ P} ^u} _v}} = {\overset{u\downarrow v\rightarrow}{\left[\begin{array}{cc} \frac{{{{\frac{\partial h}{\partial x}}^{2}}} {{\left({{-{1}} + {{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}\right)}}}{{1}{-{{{4}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{4}} {{{\frac{\partial h}{\partial x}}^{4}}}}}& \frac{{{\frac{\partial h}{\partial x}}} {{\left({{1}{-{{\frac{\partial h}{\partial x}}^{2}}}}\right)}}}{{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\\ -{\frac{\frac{\partial h}{\partial x}}{{1}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}& \frac{{1} + {{\frac{\partial h}{\partial x}}^{4}}{-{{{2}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\end{array}\right]}}$
$\perp \nabla_u n_v = $$\overset{a\downarrow b\rightarrow}{\left[\begin{array}{cc} \frac{{{{\frac{\partial h}{\partial x}}^{2}}} {{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\left({{1}{-{{{13}} {{{\frac{\partial h}{\partial x}}^{2}}}}}{-{{{64}} {{{\frac{\partial h}{\partial x}}^{14}}}}} + {{{256}} {{{\frac{\partial h}{\partial x}}^{12}}}} + {{{72}} {{{\frac{\partial h}{\partial x}}^{4}}}} + {{{400}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{432}} {{{\frac{\partial h}{\partial x}}^{10}}}}}{-{{{220}} {{{\frac{\partial h}{\partial x}}^{6}}}}}}\right)}}}{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{128}} {{{\frac{\partial h}{\partial x}}^{14}}}}}{-{{{14}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{448}} {{{\frac{\partial h}{\partial x}}^{12}}}} + {{{84}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{280}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{560}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{672}} {{{\frac{\partial h}{\partial x}}^{10}}}}}}\right)}}}& \frac{{{\frac{\partial h}{\partial x}}} {{\left({{-{1}} + {{{13}} {{{\frac{\partial h}{\partial x}}^{2}}}}{-{{{73}} {{{\frac{\partial h}{\partial x}}^{4}}}}}{-{{{32}} {{{\frac{\partial h}{\partial x}}^{16}}}}} + {{{176}} {{{\frac{\partial h}{\partial x}}^{14}}}}{-{{{416}} {{{\frac{\partial h}{\partial x}}^{12}}}}}{-{{{450}} {{{\frac{\partial h}{\partial x}}^{8}}}}} + {{{231}} {{{\frac{\partial h}{\partial x}}^{6}}}} + {{{552}} {{{\frac{\partial h}{\partial x}}^{10}}}}}\right)}} {{\frac{\partial^ 2 h}{\partial x^ 2}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{2}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{32}} {{{\frac{\partial h}{\partial x}}^{10}}}}}{-{{{10}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{40}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{80}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{80}} {{{\frac{\partial h}{\partial x}}^{8}}}}}\right)}}}\\ \frac{{{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\left({{-{1}} + {{{11}} {{{\frac{\partial h}{\partial x}}^{2}}}} + {{{16}} {{{\frac{\partial h}{\partial x}}^{14}}}}{-{{{51}} {{{\frac{\partial h}{\partial x}}^{4}}}}} + {{{129}} {{{\frac{\partial h}{\partial x}}^{6}}}}{-{{{80}} {{{\frac{\partial h}{\partial x}}^{12}}}}}{-{{{192}} {{{\frac{\partial h}{\partial x}}^{8}}}}} + {{{168}} {{{\frac{\partial h}{\partial x}}^{10}}}}}\right)}} {{\frac{\partial h}{\partial x}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{2}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{8}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{16}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{32}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{24}} {{{\frac{\partial h}{\partial x}}^{4}}}}}\right)}}}& \frac{{{\left({{1}{-{{{13}} {{{\frac{\partial h}{\partial x}}^{2}}}}}{-{{{16}} {{{\frac{\partial h}{\partial x}}^{18}}}}} + {{{74}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{242}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{501}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{681}} {{{\frac{\partial h}{\partial x}}^{10}}}}}{-{{{344}} {{{\frac{\partial h}{\partial x}}^{14}}}}} + {{{112}} {{{\frac{\partial h}{\partial x}}^{16}}}} + {{{608}} {{{\frac{\partial h}{\partial x}}^{12}}}}}\right)}} {{\frac{\partial^ 2 h}{\partial x^ 2}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{3}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{8}} {{{\frac{\partial h}{\partial x}}^{6}}}}}{-{{{6}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{12}} {{{\frac{\partial h}{\partial x}}^{4}}}}}\right)}}}\end{array}\right]}$
${{{ K} _u} _v} = {\overset{u\downarrow v\rightarrow}{\left[\begin{array}{cc} \frac{{{{\frac{\partial h}{\partial x}}^{2}}} {{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\left({{-{1}} + {{{13}} {{{\frac{\partial h}{\partial x}}^{2}}}} + {{{64}} {{{\frac{\partial h}{\partial x}}^{14}}}}{-{{{256}} {{{\frac{\partial h}{\partial x}}^{12}}}}}{-{{{72}} {{{\frac{\partial h}{\partial x}}^{4}}}}}{-{{{400}} {{{\frac{\partial h}{\partial x}}^{8}}}}} + {{{432}} {{{\frac{\partial h}{\partial x}}^{10}}}} + {{{220}} {{{\frac{\partial h}{\partial x}}^{6}}}}}\right)}}}{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{128}} {{{\frac{\partial h}{\partial x}}^{14}}}}}{-{{{14}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{448}} {{{\frac{\partial h}{\partial x}}^{12}}}} + {{{84}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{280}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{560}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{672}} {{{\frac{\partial h}{\partial x}}^{10}}}}}}\right)}}}& \frac{{{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\left({{1} + {{{512}} {{{\frac{\partial h}{\partial x}}^{24}}}}{-{{{21}} {{{\frac{\partial h}{\partial x}}^{2}}}}}{-{{{1159}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{201}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{26624}} {{{\frac{\partial h}{\partial x}}^{18}}}}} + {{{4482}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{34848}} {{{\frac{\partial h}{\partial x}}^{14}}}}} + {{{36288}} {{{\frac{\partial h}{\partial x}}^{16}}}} + {{{24192}} {{{\frac{\partial h}{\partial x}}^{12}}}}{-{{{3840}} {{{\frac{\partial h}{\partial x}}^{22}}}}} + {{{13056}} {{{\frac{\partial h}{\partial x}}^{20}}}}{-{{{12240}} {{{\frac{\partial h}{\partial x}}^{10}}}}}}\right)}} {{\frac{\partial h}{\partial x}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{2}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{512}} {{{\frac{\partial h}{\partial x}}^{18}}}}}{-{{{18}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{144}} {{{\frac{\partial h}{\partial x}}^{4}}}} + {{{2304}} {{{\frac{\partial h}{\partial x}}^{16}}}}{-{{{4608}} {{{\frac{\partial h}{\partial x}}^{14}}}}}{-{{{672}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{2016}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{4032}} {{{\frac{\partial h}{\partial x}}^{10}}}}} + {{{5376}} {{{\frac{\partial h}{\partial x}}^{12}}}}}\right)}}}\\ \frac{{{\frac{\partial h}{\partial x}}} {{\left({{1} + {{{512}} {{{\frac{\partial h}{\partial x}}^{24}}}}{-{{{21}} {{{\frac{\partial h}{\partial x}}^{2}}}}}{-{{{1159}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{201}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{26624}} {{{\frac{\partial h}{\partial x}}^{18}}}}} + {{{4482}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{34848}} {{{\frac{\partial h}{\partial x}}^{14}}}}} + {{{36288}} {{{\frac{\partial h}{\partial x}}^{16}}}} + {{{24192}} {{{\frac{\partial h}{\partial x}}^{12}}}}{-{{{3840}} {{{\frac{\partial h}{\partial x}}^{22}}}}} + {{{13056}} {{{\frac{\partial h}{\partial x}}^{20}}}}{-{{{12240}} {{{\frac{\partial h}{\partial x}}^{10}}}}}}\right)}} {{\frac{\partial^ 2 h}{\partial x^ 2}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{2}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{512}} {{{\frac{\partial h}{\partial x}}^{18}}}}}{-{{{18}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{144}} {{{\frac{\partial h}{\partial x}}^{4}}}} + {{{2304}} {{{\frac{\partial h}{\partial x}}^{16}}}}{-{{{4608}} {{{\frac{\partial h}{\partial x}}^{14}}}}}{-{{{672}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{2016}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{4032}} {{{\frac{\partial h}{\partial x}}^{10}}}}} + {{{5376}} {{{\frac{\partial h}{\partial x}}^{12}}}}}\right)}}}& \frac{{{\left({{-{1}} + {{{13}} {{{\frac{\partial h}{\partial x}}^{2}}}} + {{{16}} {{{\frac{\partial h}{\partial x}}^{18}}}}{-{{{74}} {{{\frac{\partial h}{\partial x}}^{4}}}}} + {{{242}} {{{\frac{\partial h}{\partial x}}^{6}}}}{-{{{501}} {{{\frac{\partial h}{\partial x}}^{8}}}}} + {{{681}} {{{\frac{\partial h}{\partial x}}^{10}}}} + {{{344}} {{{\frac{\partial h}{\partial x}}^{14}}}}{-{{{112}} {{{\frac{\partial h}{\partial x}}^{16}}}}}{-{{{608}} {{{\frac{\partial h}{\partial x}}^{12}}}}}}\right)}} {{\frac{\partial^ 2 h}{\partial x^ 2}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{3}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{8}} {{{\frac{\partial h}{\partial x}}^{6}}}}}{-{{{6}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{12}} {{{\frac{\partial h}{\partial x}}^{4}}}}}\right)}}}\end{array}\right]}}$
${{{ K} ^u} _v} = {\overset{u\downarrow v\rightarrow}{\left[\begin{array}{cc} \frac{{{{\frac{\partial h}{\partial x}}^{2}}} {{\frac{\partial^ 2 h}{\partial x^ 2}}} {{\left({{-{1}}{-{{{64}} {{{\frac{\partial h}{\partial x}}^{16}}}}} + {{{14}} {{{\frac{\partial h}{\partial x}}^{2}}}}{-{{{85}} {{{\frac{\partial h}{\partial x}}^{4}}}}} + {{{292}} {{{\frac{\partial h}{\partial x}}^{6}}}}{-{{{688}} {{{\frac{\partial h}{\partial x}}^{12}}}}} + {{{320}} {{{\frac{\partial h}{\partial x}}^{14}}}} + {{{832}} {{{\frac{\partial h}{\partial x}}^{10}}}}{-{{{620}} {{{\frac{\partial h}{\partial x}}^{8}}}}}}\right)}}}{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{-{1}}{-{{{128}} {{{\frac{\partial h}{\partial x}}^{16}}}}}{-{{{98}} {{{\frac{\partial h}{\partial x}}^{4}}}}} + {{{15}} {{{\frac{\partial h}{\partial x}}^{2}}}} + {{{576}} {{{\frac{\partial h}{\partial x}}^{14}}}} + {{{364}} {{{\frac{\partial h}{\partial x}}^{6}}}} + {{{1232}} {{{\frac{\partial h}{\partial x}}^{10}}}}{-{{{1120}} {{{\frac{\partial h}{\partial x}}^{12}}}}}{-{{{840}} {{{\frac{\partial h}{\partial x}}^{8}}}}}}\right)}}}& \frac{{{\frac{\partial h}{\partial x}}} {{\left({{1} + {{{5641}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{512}} {{{\frac{\partial h}{\partial x}}^{26}}}}}{-{{{22}} {{{\frac{\partial h}{\partial x}}^{2}}}}}{-{{{62912}} {{{\frac{\partial h}{\partial x}}^{18}}}}} + {{{4352}} {{{\frac{\partial h}{\partial x}}^{24}}}} + {{{222}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{16722}} {{{\frac{\partial h}{\partial x}}^{10}}}}}{-{{{1360}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{39680}} {{{\frac{\partial h}{\partial x}}^{20}}}}{-{{{16896}} {{{\frac{\partial h}{\partial x}}^{22}}}}} + {{{36432}} {{{\frac{\partial h}{\partial x}}^{12}}}}{-{{{59040}} {{{\frac{\partial h}{\partial x}}^{14}}}}} + {{{71136}} {{{\frac{\partial h}{\partial x}}^{16}}}}}\right)}} {{\frac{\partial^ 2 h}{\partial x^ 2}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{2}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{-{1}} + {{{19}} {{{\frac{\partial h}{\partial x}}^{2}}}}{-{{{512}} {{{\frac{\partial h}{\partial x}}^{20}}}}}{-{{{162}} {{{\frac{\partial h}{\partial x}}^{4}}}}} + {{{2816}} {{{\frac{\partial h}{\partial x}}^{18}}}}{-{{{6912}} {{{\frac{\partial h}{\partial x}}^{16}}}}} + {{{816}} {{{\frac{\partial h}{\partial x}}^{6}}}} + {{{6048}} {{{\frac{\partial h}{\partial x}}^{10}}}}{-{{{9408}} {{{\frac{\partial h}{\partial x}}^{12}}}}}{-{{{2688}} {{{\frac{\partial h}{\partial x}}^{8}}}}} + {{{9984}} {{{\frac{\partial h}{\partial x}}^{14}}}}}\right)}}}\\ \frac{{{\frac{\partial h}{\partial x}}} {{\left({{1} + {{{512}} {{{\frac{\partial h}{\partial x}}^{24}}}}{-{{{21}} {{{\frac{\partial h}{\partial x}}^{2}}}}}{-{{{1159}} {{{\frac{\partial h}{\partial x}}^{6}}}}} + {{{201}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{26624}} {{{\frac{\partial h}{\partial x}}^{18}}}}} + {{{4482}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{34848}} {{{\frac{\partial h}{\partial x}}^{14}}}}} + {{{36288}} {{{\frac{\partial h}{\partial x}}^{16}}}} + {{{24192}} {{{\frac{\partial h}{\partial x}}^{12}}}}{-{{{3840}} {{{\frac{\partial h}{\partial x}}^{22}}}}} + {{{13056}} {{{\frac{\partial h}{\partial x}}^{20}}}}{-{{{12240}} {{{\frac{\partial h}{\partial x}}^{10}}}}}}\right)}} {{\frac{\partial^ 2 h}{\partial x^ 2}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{2}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{19}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{512}} {{{\frac{\partial h}{\partial x}}^{20}}}} + {{{162}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{2816}} {{{\frac{\partial h}{\partial x}}^{18}}}}} + {{{6912}} {{{\frac{\partial h}{\partial x}}^{16}}}}{-{{{816}} {{{\frac{\partial h}{\partial x}}^{6}}}}}{-{{{6048}} {{{\frac{\partial h}{\partial x}}^{10}}}}} + {{{9408}} {{{\frac{\partial h}{\partial x}}^{12}}}} + {{{2688}} {{{\frac{\partial h}{\partial x}}^{8}}}}{-{{{9984}} {{{\frac{\partial h}{\partial x}}^{14}}}}}}\right)}}}& \frac{{{\left({{-{1}} + {{{13}} {{{\frac{\partial h}{\partial x}}^{2}}}} + {{{16}} {{{\frac{\partial h}{\partial x}}^{18}}}}{-{{{74}} {{{\frac{\partial h}{\partial x}}^{4}}}}} + {{{242}} {{{\frac{\partial h}{\partial x}}^{6}}}}{-{{{501}} {{{\frac{\partial h}{\partial x}}^{8}}}}} + {{{681}} {{{\frac{\partial h}{\partial x}}^{10}}}} + {{{344}} {{{\frac{\partial h}{\partial x}}^{14}}}}{-{{{112}} {{{\frac{\partial h}{\partial x}}^{16}}}}}{-{{{608}} {{{\frac{\partial h}{\partial x}}^{12}}}}}}\right)}} {{\frac{\partial^ 2 h}{\partial x^ 2}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{3}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{1}{-{{{7}} {{{\frac{\partial h}{\partial x}}^{2}}}}} + {{{8}} {{{\frac{\partial h}{\partial x}}^{8}}}} + {{{18}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{20}} {{{\frac{\partial h}{\partial x}}^{6}}}}}}\right)}}}\end{array}\right]}}$
${K} = {\frac{{{\left({{1}{-{{{29}} {{{\frac{\partial h}{\partial x}}^{2}}}}}{-{{{4096}} {{{\frac{\partial h}{\partial x}}^{34}}}}} + {{{394}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{231424}} {{{\frac{\partial h}{\partial x}}^{30}}}}} + {{{45056}} {{{\frac{\partial h}{\partial x}}^{32}}}} + {{{19605}} {{{\frac{\partial h}{\partial x}}^{8}}}} + {{{284000}} {{{\frac{\partial h}{\partial x}}^{12}}}} + {{{2664192}} {{{\frac{\partial h}{\partial x}}^{24}}}}{-{{{3322112}} {{{\frac{\partial h}{\partial x}}^{22}}}}} + {{{737280}} {{{\frac{\partial h}{\partial x}}^{28}}}}{-{{{3330}} {{{\frac{\partial h}{\partial x}}^{6}}}}}{-{{{85305}} {{{\frac{\partial h}{\partial x}}^{10}}}}}{-{{{2486000}} {{{\frac{\partial h}{\partial x}}^{18}}}}} + {{{1519760}} {{{\frac{\partial h}{\partial x}}^{16}}}}{-{{{1632000}} {{{\frac{\partial h}{\partial x}}^{26}}}}} + {{{3232768}} {{{\frac{\partial h}{\partial x}}^{20}}}}{-{{{738760}} {{{\frac{\partial h}{\partial x}}^{14}}}}}}\right)}} {{\frac{\partial^ 2 h}{\partial x^ 2}}}}{{{{\left({{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}\right)}^{3}}} {{\sqrt{{1} + {{{2}} {{{\frac{\partial h}{\partial x}}^{4}}}}{-{{{3}} {{{\frac{\partial h}{\partial x}}^{2}}}}}}}} {{\left({{-{1}}{-{{{1024}} {{{\frac{\partial h}{\partial x}}^{24}}}}} + {{{22}} {{{\frac{\partial h}{\partial x}}^{2}}}}{-{{{221}} {{{\frac{\partial h}{\partial x}}^{4}}}}}{-{{{22784}} {{{\frac{\partial h}{\partial x}}^{20}}}}} + {{{7168}} {{{\frac{\partial h}{\partial x}}^{22}}}} + {{{1340}} {{{\frac{\partial h}{\partial x}}^{6}}}}{-{{{32928}} {{{\frac{\partial h}{\partial x}}^{12}}}}} + {{{15744}} {{{\frac{\partial h}{\partial x}}^{10}}}} + {{{50304}} {{{\frac{\partial h}{\partial x}}^{14}}}} + {{{43520}} {{{\frac{\partial h}{\partial x}}^{18}}}}{-{{{55680}} {{{\frac{\partial h}{\partial x}}^{16}}}}}{-{{{5460}} {{{\frac{\partial h}{\partial x}}^{8}}}}}}\right)}}}}$