Differentialquotient

Übergang vom Differenzenquotient zum Differentialquotient

Verschieben Sie den Punkt B zum Punkt A und beobachten, wie sich der Differenzenquotient ändert.

f(x) = x^(2)
A = Point(f)
B = Point(f)
a = Line(A, B)
m = Slope(a)
b = OrthogonalLine(B, xAxis)
c = OrthogonalLine(A, xAxis)
x_0 = Intersect(c, xAxis)
x_1 = Intersect(b, xAxis)
d = OrthogonalLine(A, yAxis)
e = OrthogonalLine(B, yAxis)
E = Intersect(e, yAxis)
F = Intersect(yAxis, d)
G = Intersect(b, d)
abstandAG = Distance(A, G)
abstandGB = Distance(G, B)
deltay: abstandGB
deltax: abstandAG
differenzenquotient: deltay / deltax
g = Segment(B, G)
h = Segment(G, x_1)
i = Segment(A, x_0)
j = Segment(A, G)
k = Segment(F, A)
l = Segment(E, B)
TextAG: "\Delta x\,=\,x_1-x_0\, = \, " + (LaTeX[abstandAG]) + ""
TextGB: "\Delta y\,=\,f(x_1)-f(x_0) \, = \, " + (LaTeX[abstandGB]) + ""
n = Segment(x_0, x_1)
p = Segment(E, F)
abstandCD = Distance(x_0, x_1)
TextCD: "\Delta x= x_1 -x_0 = \, " + (LaTeX[abstandCD]) + ""
abstandEF = Distance(E, F)
TextEF: "\Delta y = f(x_1) -f(x_0) = \, " + (LaTeX[abstandEF]) + ""
Text1: "Differenzenquotient: $ \frac{\Delta y}{\Delta x}=\frac{f(x_1)-f(x_0)}{x_1-x_0} $=" + (LaTeX[differenzenquotient]) + ""
q = Tangent(A, f)
m_1 = Slope(q)
Text2: "Differentialquotient f'(x_0)=" + m_1 + ""