$\exp$

$\ln$

$Q(x|\underbrace{\ln(x)}_{y})$

$P(\underbrace{y}_{\ln(x)}|\underbrace{e^{y}}_{x})$

e-Funktion

ln-Funktion

y = x

$x$ 

$\underbrace{\ln(x)}_{y}$

$\underbrace{e^{y}}_{x}$

$\underbrace{y}_{\ln(x)}$

$1$

$f'(y) = e^{y} = x$

$1$

$x$

$x$

$1$

g'(x) = \frac{1}{x}

Ableitung der e-Funktion

Ableitung der ln-Funktion

f(x) = ℯ^(x)
g(x) = ln(x)
Q = Point(g)
P: (y(Q) | x(Q))
XP: (x(P) | 0)
YP: (0 | y(P))
u = Vector(P, YP)
L = -5 (slider from -10 to 5, step 0.1)
U: (x(P) + 1 | y(P))
XQ: (x(Q) | 0)
YQ: (0 | y(Q))
i = Segment(XQ, Q)
w = Vector(Q, YQ)
PosYln = If(y(P) ≥ 1, (-2.4 | y(P) + 0.3), (0.2 | y(P) + 0.3))
PosXln: (x(P) - 0.5 | -0.3)
PosXln2: (x(Q) - 0.5 | -0.3)
PosX: (x(P) - 0.5 | -0.3)
PosY = If(y(P) ≥ 1, (-1.5 | y(P) + 0.3), (0.2 | y(P) + 0.3))
a = false
b = true
c = Vector(Q, XQ)
PosYln2: (-1.3 | y(Q) + 0.3)
PosY2: (-2.5 | y(Q) + 0.3)
PosX2: (x(Q) - 0.5 | -0.3)
p: y = x
tf = Tangent(P, f)
mf = Slope(tf)
tg = Tangent(Q, g)
S: (x(Q) | y(Q) + 1)
mg = Slope(tg)
T: (x(Q) + mf | y(S))
V: (x(U) | y(P) + mf)
vPU = Vector(P, U)
vUV = Vector(U, V)
vQS = Vector(Q, S)
vST = Vector(S, T)
v = Segment(XP, P)
h = Vector(P, YP)
d = Vector(Q, (x(T) | y(Q)))
e = Vector((x(T) | y(Q)), T)
m = false
n = false