λ

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$\textcolor{#3333CC}{f(x,y)=}$

f(x, y) = sin((x * y)) + sin(x) + cos(y)
f'_{y} = Derivative(f, y)
f'_{x} = Derivative(f, x)
f': {{f'_{x}, f'_{y}}}
factor = 1 (slider from -1 to 1, step 2)
n = 0 (slider from 0 to 30, step 1)
X_{0} = PointIn(xOyPlane)
F: X_{0} + (0, 0, f(X_{0}))
X_{i} = PointIn(xOyPlane)
F_{i}: X_{i} + (0, 0, f(X_{i}))
λ_{0} = 1 (slider from 0.01 to 5, step 0.01)
X_{next}: X_{i} + ((factor * λ_{0}) * (f'_{x}(X_{i}), f'_{y}(X_{i})))
L: {}
textStep: "\text{Schritt }\textcolor{#3333CC}{" + (LaTeX[n]) + "}"
v_{n} = Vector(X_{i}, X_{next})
g = Segment(X_{0}, F)
h = Segment(F_{i}, X_{i})
Eingabefeld1 = Textfield(f)
L_{y} = Sequence((x(Element[L, k]), y(Element[L, k]), f(Element[L, k])), k, 1, Length[L])
L_{lines} = Sequence(Segment[Element[L, k], Element[L_{y}, k]], k, 1, Length[L])
L_{nexts} = If(n > 0, Append[Sequence[Vector[Element[L, k], Element[L, k + 1]], k, 1, Length[L] - 1], Vector[Element[L, Length[L]], X_{i}]], {})
F_{next}: X_{next} + (0, 0, f(X_{next}))
i = Segment(X_{next}, F_{next})
textCurrent: "f(\textcolor{#3333CC}{x_{" + (LaTeX[n]) + "}})=f(" + (LaTeX[x(X_{i})]) + "," + (LaTeX[y(X_{i})]) + ")=" + (LaTeX[z(F_{i})]) + ""
textNext: "f(\textcolor{#CC0000}{x_{" + (LaTeX[n + 1]) + "}})=f(" + (LaTeX[x(X_{next})]) + "," + (LaTeX[y(X_{next})]) + ")=" + (LaTeX[z(F_{next})]) + ""
X_{i2}: X_{i}