\scalebox{1} \text{Ableitung als Tangentensteigung}

\scalebox{0.9} \text{Werner Knobloch, 2011

Übe diese Methode als schnelle Grobskizze der Ableitung auf Papier für beliebige Funktionskurven

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t = -1.42 (slider from -3 to 1.5, step 0.01)
a = 1.4 (slider from -5 to 5, step 0.1)
b = 4.1 (slider from -5 to 5, step 0.1)
c = 1.1 (slider from -5 to 5, step 0.1)
d = -2.3 (slider from -5 to 5, step 0.1)
e = 0 (slider from -5 to 5, step 1)
f(x) = (a * x^(4)) + (b * x^(3)) + (c * x^(2)) + (d * x) + e
A: (t, f(t))
t_1 = Tangent(A, f)
g = Slope(t_1)
B: (x(A) + 2, y(A))
C: (x(A) - 2, y(A))
i = Segment(C, B)
α = Angle(i, t_1)
h: tan(α)
D: (x(A), h)
f'(x) = f'(x)
Ableitungskurve = false
E: (x(A), 0)
j = Segment(A, E)
Text3 = LaTeX(f, true, true)
k = Segment(D, E)
Animationstempo = 0 (slider from 0 to 1, step 0.1)
Text4: "x=   " + (LaTeX[x(A)]) + ""
Text1: "\scalebox{0.9}{tan(" + (LaTeX[α]) + ") = f'(" + (LaTeX[x(A)]) + ") =" + (LaTeX[f'(x(A))]) + " }"
Text2: "\scalebox{0.9} {f'(x)= tan(α(x)) =" + (LaTeX[f']) + "}"