Find a mistake type of math problems I am interested in the problems where the formulation of the problem has some kind of mistake in it and as a consequence gives unexpected answer.
Can't explain it better than this example:
For example: $4^2 = 4 \cdot 4 = 4+ 4 + 4+4$ (sum $4$ times)
Similarly: $$\frac{d}{dx}x^2=\frac{d}{dx}(x\cdot x)=\frac{d}{dx}(x+x+...+x) = 1 + 1 + ... + 1 = x$$
Since the $1$'s are summed $x$ times. I hope you see what went wrong :) If you have encountered problems of this type, please share.
EDIT:  I am aware that my proposed example has a mathematically inconsistent step, this type of expansion is only allowed for natural numbers making the function non-differentiable. However this is the kind of inconsistencies I find amusing.

$(-32)^{\frac{1}{5}}\neq(-32)^{\frac{2}{10}}$:


*

*$(-32)^{\frac{1}{5}}=\sqrt[5]{(-32)^1}=\sqrt[5]{-32}=-2$

*$(-32)^{\frac{2}{10}}=\sqrt[10]{(-32)^2}=\sqrt[10]{1024}=\pm2$
