Comment dériver des nombres ? Partie III

RD:
R→Rx, y ∈R
D(x, y) = D(x).y +x.D(y)
D(1) D(−1) D(0)
D(−n)n∈N
D(a1a2a3)
D(a1a2a3a4)
D(a1. . . an)
n∈N
n= Πk
1=1pαi
i,
piαi
D(n)
p D(p) = 1

D(n)
D(60)
D(aq)a∈R∗q∈Z
x∈QD(x)
D(1/2) D(1/3) D(3/4)
a, b ∈ZD(a)D(b)
D(a/b)
p p p+2
p+ 2
p2p
D(x) = p+ 2
D2(x)=1

R
D
k
Y
i=1
pαi
i
piαi∈Qi= 1, . . . , k
k
Y
i=1
pαi
i= 1 α1=α2=··· =αk= 0
x∈ D
D(ay)y∈Qa∈R∗
x∈ D
D(√3)