query: Differentiation of $x^{2}$ by writing it as $ x \: + \: x \: + \: ... \: + \: ... \: + \: x \: \: (\text{as many as x}) $ gives paradox $2=1$
positive_passages.docid: 152895
positive_passages.text: What is wrong with this derivation of $\frac{d}{dx}x^2$?
negative_passages.docid: 41779
negative_passages.text: Is $x/x$ equal to $1$
negative_passages.docid: 124121
negative_passages.text: Is this logic behind the derivative of $x^x$ a coincidence?
negative_passages.docid: 117978
negative_passages.text: differentiation using formal definition i.e. $(x+h)$
negative_passages.docid: 67588
negative_passages.text: Why does $|e^{ix}|^2 = 1$?
negative_passages.docid: 973
negative_passages.text: Is the property "being a derivative" preserved under multiplication and composition?
negative_passages.docid: 157417
negative_passages.text: Understanding the definition of a multiple (double) root
negative_passages.docid: 157918
negative_passages.text: Finding the derivative of $x^x$
negative_passages.docid: 136933
negative_passages.text: Which $n$ can be expressed as $x^2 − y^2$?
negative_passages.docid: 28297
negative_passages.text: derivative of x^x^x... to infinity?
negative_passages.docid: 132169
negative_passages.text: $x^{2000} + \frac{1}{x^{2000}}$ in terms of $x + \frac 1x$.
negative_passages.docid: 36990
negative_passages.text: Notation of the second derivative - Where does the d go?
negative_passages.docid: 91521
negative_passages.text: Ambiguity of notation: $\sin(x)^2$
negative_passages.docid: 1002
negative_passages.text: Where is the flaw in this "proof" that 1=2? (Derivative of repeated addition)
negative_passages.docid: 40549
negative_passages.text: How to proof the the derivative of $x^2$ is $2x$?
negative_passages.docid: 139322
negative_passages.text: Derivative of a factorial
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$