query: Why $2x$? Can't it be $x$?
positive_passages.docid: 1002
positive_passages.text: Where is the flaw in this "proof" that 1=2? (Derivative of repeated addition)
negative_passages.docid: 69187
negative_passages.text: What's my confusion with the chain rule? (Differentiating $x^x$)
negative_passages.docid: 124121
negative_passages.text: Is this logic behind the derivative of $x^x$ a coincidence?
negative_passages.docid: 53958
negative_passages.text: General misconception about $\sqrt x$
negative_passages.docid: 82630
negative_passages.text: How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$?
negative_passages.docid: 158610
negative_passages.text: Why is the differentiation of $e^x$ is $e^x$?
negative_passages.docid: 102138
negative_passages.text: Why does $\sqrt{x^2}$ seem to equal $x$ and not $|x|$ when you multiply the exponents?
negative_passages.docid: 17265
negative_passages.text: Intuition for why equations of the form $k^x=x^c$ are not solvable trivially?
negative_passages.docid: 35750
negative_passages.text: Where did $-4x$ come from?
negative_passages.docid: 82586
negative_passages.text: Why is cos -x equal to cos x?
negative_passages.docid: 132113
negative_passages.text: Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function?
negative_passages.docid: 148556
negative_passages.text: Could you explain why $\frac{d}{dx} e^x = e^x$ "intuitively"?
negative_passages.docid: 24307
negative_passages.text: Is $x^x=y$ solvable for $x$?
negative_passages.docid: 41182
negative_passages.text: What does the construct x = x || y mean?
negative_passages.docid: 96554
negative_passages.text: Why is $x^0 = 1$ except when $x = 0$?
negative_passages.docid: 154327
negative_passages.text: $A^2X = X$ show that $AX = X$, if $A_{ij} > 0$ and $x_{i} > 0$
negative_passages.docid: 122948
negative_passages.text: $x^{x^{x^{\dots}}}=2$, what is the value of $x$?