x'(t)=a\, x(t)

x(t)= ℯ ^{at}

f(x)= ℯ ^{a x}

f'(x)=a\, f(x)

t = 2.5 (slider from -5 to 5, step 0.5)
a = 0.5 (slider from -5 to 5, step 0.1)
f(x) = exp((a * x))
tang(x) = (f'(t) * (x - t)) + f(t)
h(x) = sqrt((f'(x))^(2) / ((f'(x))^(2) + 1))
A: (t, f(t))
g = Tangent(A, f)
A': (t + h(t), tang(t + h(t)))
u = Vector(A, A')
O = Intersect(xAxis, yAxis)
C = Point(xAxis)
v = Vector(O, C)
X: (ℯ^((a * t)), 0)
X_v: (f(t) + (a * f(t)), 0)
w = Vector(X, X_v)
A_x: (t, 0)
b = Vector(A_x, A)
c = Vector(O, X)
d = Vector((1, 0), (1 + a, 0))
e = Vector((0, 1), (h(0), (a * h(0)) + 1))
i = Vector(O, (0, 1))
B = (3.8606666666666674, 3.5213333333333328)
D = (4.994, 3.5213333333333328)