Le nombre dérivé
Author: G. Amenta

Afficher la fonction dérivée

Afficher le coefficient directeur

Choix = 1 (slider from 1 to 6, step 1)
x_0 = Point(xAxis)
liste: {x^(2) / 2, x^(3) / 6, x^(4) / 8, sin(x), sqrt(x), cbrt(x)}
f = Element(liste, Choix)
f' = Derivative(f)
x_1 = Point(xAxis)
a_1 = OrthogonalLine(x_1, xAxis)
B = Intersect(f, a_1, 1)
b = OrthogonalLine(B, yAxis)
c = OrthogonalLine(x_0, xAxis)
D = Intersect(f, c, 1)
a = Line(B, D)
e = Segment(B, x_1)
g = Segment(D, x_0)
text1: "Le\;coefficient\;directeur\;de\;la\;droite\;a\;est\; \frac{ Δy }{Δx }\;= \frac{ " + (y(B)) + "\;-\;" + (y(D)) + " }{" + (x(B)) + "\;-\;" + (x(D)) + " }\;=\;" + (Slope[a])
text2: "Ainsi,\;\[\lim_{x_1\rightarrow x_0}  \frac{ Δy }{Δx }\;=\; " + (f'(x(x_0)))
text3: "f(x) = " + f
text4: "f'(x)\;=\;" + f'
d = false
A = Intersect(f', c, 1)
h = OrthogonalLine(A, yAxis)
f_{x_0} = Intersect(h, yAxis)
i = Segment(x_0, A)
j = Segment(A, f_{x_0})
text5: "f'(x_0) = " + (f'(x(x_0)))
k = false