query: all functions that uphold $f'(x)=f(1/x)$
positive_passages.docid: 23485
positive_passages.text: Solving $\forall x \in \mathbb{R}_+^*, f'(x) = f\left(\frac1{x}\right)$
negative_passages.docid: 55175
negative_passages.text: Is the function $f(x) = x^2 - 2x$ one-to-one?
negative_passages.docid: 106284
negative_passages.text: Establishing a Basis for $F[x]/(f(x))$
negative_passages.docid: 99906
negative_passages.text: If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
negative_passages.docid: 51291
negative_passages.text: How can I express $\int \frac{1}{f'(x)}$ in terms of $f(x)$
negative_passages.docid: 144323
negative_passages.text: Differentiation of a function
negative_passages.docid: 1440
negative_passages.text: Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
negative_passages.docid: 4065
negative_passages.text: What are the entire functions $f$ such that $|f'(z)| \leq |f(z)| \ ? $
negative_passages.docid: 139019
negative_passages.text: Polynomial satisfying $f(x) = f'(x) \cdot f''(x)$
negative_passages.docid: 1641
negative_passages.text: Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
negative_passages.docid: 99894
negative_passages.text: Does there exists an entire function $f$ such that $f(0)=1$ and $|f(z)|\leq \frac{1}{|z|} $ for all $|z|\geq 5$?
negative_passages.docid: 98356
negative_passages.text: There does not exist an entire function which satisfies $f({1\over n})={1\over 2^n}$?
negative_passages.docid: 17343
negative_passages.text: Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
negative_passages.docid: 138544
negative_passages.text: For which values of $x$, will $f (x) . f '(x) < 0$?
negative_passages.docid: 56958
negative_passages.text: bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
negative_passages.docid: 44148
negative_passages.text: Functions that are their own inverse.