A proof that $1=2$. May I know why it’s false?

Question

im not good at formatting. May I know why it’s false

$x^2= x+x+x+\ldots(x\; \text{times})$

apply derivative on both sides

$=> \frac{d}{dx}(x^2)=\frac{d}{dx}(x+x+x+\ldots(x\; \text{times}))$

$=> 2x=1+1+1+\ldots(x\; \text{times})$

$=> 2x=x$

$=> 2=1$

Answer 1

You cannot add '$x$', $x$ number of times without knowing what $x$ exactly is. Hence the differentiation on the RHS has no real meaning.

This fails for many cases like:

$1)$ '$x$' is not an integer.

$2)$ Dependency of $x$ on $x$ which you are not considering when differentiating on RHS.

Answer 2

This has been asked twice or thrice already. Two problems might be pointed out

$(1)$ "$x$ times" is ill-defined for non integer values of $x$; and even so

$(2)$ "$x$ times" is also a function of $x$, which you're ignoring