u(x)

v(x)

f(x)

\underbrace{f(x) }{}= \underbrace{u(x)}{} + \underbrace{v(x)}{}

\underbrace{f(x+h) - f(x)}{} = \underbrace{u(x+h) - u(x) }{}+ \underbrace{v(x+h) - v(x)}{}

\underbrace{\frac{f(x+h) - f(x)}{h}}{} = \underbrace{\frac{u(x+h) - u(x) }{h}}{}+ \underbrace{\frac{v(x+h) - v(x)}{h}}{}

Steigungen:

Änderungen:

y-Werte:

x

x+h

Ableitungen:

\underbrace{f'(x) }{}= \underbrace{u'(x)}{} + \underbrace{v'(x)}{}

g(x) = (0.1 * x^(3)) + 1
h(x) = (0.4 * x^(2)) + 2
f(x) = g(x) + h(x)
P = Point(f)
i = OrthogonalLine(P, xAxis)
A = Intersect(h, i)
B = Intersect(g, i)
j = Tangent(P, f)
k = Tangent(A, h)
b = 1 (slider from -5 to 5)
l = Tangent(B, g)
Q = Point(f)
u = Vector(P, (x(Q), y(P)))
v = Vector((x(Q), y(P)), Q)
xQ: x(Q)
w = Vector(A, (xQ, y(A)))
a = Vector((xQ, y(A)), (xQ, h(xQ)))
c = Vector(B, (xQ, y(B)))
d = Vector((xQ, y(B)), (xQ, g(xQ)))
dx: x(Q) - x(P)
m = Line(P, Q)
A1: A + w + a
n = Line(A, A1)
B1: B + c + d
p = Line(B, B1)
mf = Slope(m)
mg = Slope(p)
mh = Slope(n)
Text5: "Steigung: " + mf + ""
Text6: "Steigung: " + mh + ""
Text2: "Änderung: " + (y(v)) + ""
Text3: "Änderung: " + (y(d)) + ""
Text4: "Änderung: " + (y(a)) + ""
Text1: "Steigung:: " + mg + ""
mtf = Slope(j)
mth = Slope(k)
mtg = Slope(l)
Text7: "Steigung: " + mtf + ""
Text8: "Steigung: " + mth + ""
Text9: "Steigung: " + mtg + ""
Text11: "" + (y(P)) + ""
Text12: "" + (y(A)) + ""
Text13: "" + (y(B)) + ""
Text15: "" + (y(a)) + ""
Text16: "" + (y(d)) + ""
Text17: "" + (y(v)) + ""
Text20: "" + mf + ""
Text21: "" + mtf + ""
Text22: "" + mh + ""
Text23: "" + mth + ""
Text25: "" + mtg + ""
x0: (x(P), 0)
x1: (x(Q), 0)
e: f'(x(P))
o: g'(x(P))
q: h'(x(P))
Text30: "" + e + ""
Text31: "" + o + ""
Text32: "" + q + ""
Text24: "" + mg + ""