f(t)=(2t^2,t)

g(x,y)=x^2y+3x y^3

h=g∘f

x'=4t, \;y'=1

g_x=2x y+y^3\
g_y=x^2+9xy^2

h'=g_x \,x'+g_y\,y'

g_x\,x'\
g_y\,y'

Kettenregel

Totale\; Ableitung

ay: 1
t = 2
ax: (4 * t)
atx: (2 * t^(2))
aty: t
A: (atx, aty, 0)
g(x, y) = (x^(2) * y) + ((3 * x) * y^(3))
B: (atx, aty, g(atx, aty))
a = CurveCartesian((2 * t^(2)), t, t, -2, 10)
b = CurveCartesian((2 * t^(2)), t, (10 * t^(5)), t, -2, 10)
H: (atx + ax, aty + ay, 0)
u = Vector(A, H)
H_x: (x(H), y(A), 0)
H_y: (x(A), y(H), 0)
v = Vector(A, H_x)
w = Vector(A, H_y)
f = Segment(B, A)
B_x: (x(H_x), y(A), f)
B_y: (x(A), y(H), f)
c = Vector(B, B_x)
d = Vector(B, B_y)
g_x(x, y) = ((2 * x) * y) + (3 * y^(3))
g_y(x, y) = x^(2) + ((9 * x) * y^(2))
ex: g_x(x(A), y(A))
ey: g_y(x(A), y(A))
G_x: (x(H_x), y(H_x), f + (ex * ax))
e = Vector(B, G_x)
G_y: (x(H_y), y(H_y), f + (ey * ay))
h = Vector(B, G_y)
i: h + e
B' = Translate(B, i)
j = Vector(B, B')
k = Segment(B_x, H_x)
C = (6.989076097672907, 1.8251467614657422, 0)
D = (6.985515355944678, 1.7787796627786179, 0)
l = Segment(C, D)
m = Segment(B_y, H_y)
E = Point(k)
n = Segment(E, H)
p = Segment(H, H_y)
q = Segment(G_x, B_x)
r = Segment(G_y, B_y)
s = Segment(G_x, B')
f_1 = Segment(G_y, B')
F = (-6.195666207538843, 5.172294011848018)
G = (-4.495666207538843, 5.172294011848018)