# Math Help - finding the error in differentiation

1. ## finding the error in differentiation

Hello all,
This is a differentiaiton question given to me by my friend.I could not find the mistake in the proof.
x = x
x = 1 + 1 + ... + 1 (x times)
multiplying by x
x(x) = x(1 + 1 + ... + 1)
x2 = x + x + ... + x
D(x2) = D(x + x + ... + x)
D(x2) = D(x) + D(x) + ... + D(x)
2x = 1 + 1 + ... + 1 (x times)
2x = x
2 = 1

i think it is somewhere in the differentiation .But couldnot get it.

i hope i have not made a mistake by posting in the wrong forum.

2. Hello,

x = 1 + 1 + ... + 1 (x times)
You cannot write it unless x is a positive integer.

3. Also in "x= 1+ 1+ ...+ 1 (x times)" or " $x^2= x+ x+ x+ ...+ x$ (x times)" the number of terms in the sum is itself a function of x and the differentiation rule (f+ g)'= f'+ g' does not apply.