Whats Wrong in this? "2 = 1"

Method 1: Differentiation Method

Let a^b mean a "raised to" b

1^2 = 1
2^2 = 2 + 2
3^2 = 3 + 3 + 3

so for any X > 0

X^2 = X + X + X + ..... (X times)

Differentiate both sides with resepct to X

2X = 1 + 1 + 1 + ... (X times)

2X = X

2 = 1 .... Cancelling X from both sides as X <> 0


Method 2: Logarithm Method

We know that natural log of 2 i.e. Ln(2) = 0.6931471

As per log series transformation ....

Ln(2) = 1 - (1/2) + (1/3) - (1/4) + (1/5) .....

Ln(2) = (1 + 1/3 + 1/5 ....) - (1/2 + 1/4 + 1/6 ....)

Ln(2) = ((1 + 1/3 + 1/5 ....) + (1/2 + 1/4 + 1/6 ....)) - 2(1/2 + 1/4 + 1/6 + 1/8 ....)

Ln(2) = (1 + 1/2 + 1/3 + 1/4 ...) - (1 + 1/2 + 1/3 + 1/4 ....)

Ln(2) = 0


Now we also know Ln(1) = 0 ........ as e^0=1

So Ln(2) = Ln(1) = 0

e^Ln(2) = e^Ln(1) ......... taking the exponent of both sides

2 = 1 .............. as e^Ln(a) = a


I know for sure that the first solution can be criticized on the differentiation but what about the 2nd one....