h =1

h verkleinern

h = -1

f

P

Q

s

Ausschnittsvergrößerung

Sekante

Mikroskop

h = 0

XXXXXXXXXXX
XXXXXXXXXX

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f(x) =

x_0 =

\downarrow

f'(x_0) =

\downarrow

f'(x_0)

f'(x_0) = 

Steigung der Sekante:

f(x) = x^(2)
x0 = 1
P: (x0, f(x0))
y0: f(x0)
h = 1
x1: x0 + h
Q: (x1, f(x1))
y1: f(x1)
R: (x1, y0)
gL1: -4
gR1: 4
gU1: -5
gO1: 5
s = Line(P, Q)
g(x) = If[h > 0, (1 / h * (f((x * h) + x0) - y0)), If[h < 0, (1 / ((-h)) * (f((x * (-h)) + x0) - y0)), f(x + x0) - y0]]
P': (0, g(0))
Q' = If(h > 0, (1, g(1)), If[h < 0, (-1, g(-1)), P'])
s' = Line(P', Q')
k: 4
R': (x(Q'), y(P'))
dx: h
dy: y1 - y0
u = Vector(P', R')
v = Vector(R', Q')
Text2: "" + dx + ""
Text3: "" + dy + ""
kSekante1 = false
c = Circle(P, 1)
bMikroskop = false
rLupe: 3.7
LupeAussen(x, y) = x^(2) + y^(2) > rLupe^(2)
LupeRahmen: x^(2) + y^(2) = rLupe^(2)
gL2: -4
gR2: 4
gO2: 3
m: dy / dx
Text5: "f(x_0+h)-f(x_0) = " + (LaTeX[dy]) + ""
Text4: "h = " + (LaTeX[h]) + ""
Eingabefeld1 = Textfield(f)
Eingabefeld2 = Textfield(x0)
a: f'(x0)
b = false
zaehler = 0
Text11: "h = " + (LaTeX[h]) + ""
Text10: "m(" + (LaTeX[x0]) + "," + (LaTeX[x1]) + ") = " + (LaTeX[m]) + ""
Text12: "f'(" + (LaTeX[x0]) + ") ="
Text15: "m(x_0,x_0+h) = \dfrac{f(x_0+h)-f(x_0)}{h} = " + (LaTeX[m]) + ""
Text6: "m(x_0,x_0+h) = " + (LaTeX[m]) + ""
Text9: "h = " + (LaTeX[h]) + ""
Text14: "f'(x_0) = " + (LaTeX[a]) + ""