prechod[odkud_, kam_, kde_, tau_] := 
        a + b*Tanh[((x - kde)/tau)] /. Solve[{a + b == 1. *kam, 
                a - b == odkud}, {a, 
                b}][[1]];
Plot[prechod[-2, 4, 2, 0.1], {x, -5, 5}, 
        AxesLabel -> {"x", "prechod[x]"}, 
        PlotStyle -> {Hue[0], Thickness[0.01]}];

dpiskovec = 0.3;
dpolystyren = 0.1;
dsum = % + %%;
λpiskovec = 0.9;
λpolystyren = 0.04;
rocppolystyren = 60*1270;
rocppiskovec = 1800*720;
taunase = dsum/100;
λ = 
        prechod[λpiskovec, λpolystyren, dpiskovec, 
          taunase];
\(\(Plot[λ, {x, 0, dsum}, 
        AxesLabel -> {"x", \*""λ[W.(m^(-1)).(K^(-1))]""}, 
        PlotStyle -> {Hue[0], Thickness[0.01]}];\)\)

rce = 
        D[λ*D[T[x], x], x] == 0;
poc1 = T[0] == 20;
res[
          der_] := NDSolve[{rce,  poc1, T'[0] == der}, 
            T[x], {x, 0, dsum}][[1]];
Teplota[der_] := T[x] /. res[der];
T2[der_] := (T[x] /. res[der]) /. 
          x -> dsum;
teploty = 
        Table[Teplota[der], {der, -10, 10, 
            2}];
Plot[Evaluate[teploty], {x, 0, dsum}, PlotRange -> All, 
        AxesLabel -> {"x", "T[x]"}];

T2[-12]
T2[-13]

derivace = (Table[{T2[der], der}, {der, -13, -12, 
                0.1}] // Interpolation[#][Tt] &) /. 
        Tt -> -10

Plot[
        Evaluate[Teplota[derivace]], {x, 0, dsum}, PlotRange -> All, 
        AxesLabel -> {"x", "T[x]"}];