query: Functions whose derivative is the inverse of that function
positive_passages.docid: 16034
positive_passages.text: Function whose inverse is also its derivative?
negative_passages.docid: 134835
negative_passages.text: What is exactly the inverse of the function $f(x)=\frac{x}{1-x^2}$?
negative_passages.docid: 47166
negative_passages.text: Is there a function whose inverse is exactly the reciprocal of the function, that is $f^{-1} = \frac{1}{f}$?
negative_passages.docid: 151575
negative_passages.text: Differentiable bijection $f:\mathbb{R} \to \mathbb{R}$ with nonzero derivative whose inverse is not differentiable
negative_passages.docid: 56827
negative_passages.text: Functions that are their Own nth Derivatives for Real $n$
negative_passages.docid: 30836
negative_passages.text: Derivative of a determinant whose entries are functions
negative_passages.docid: 41043
negative_passages.text: example of discontinuous function having direction derivative
negative_passages.docid: 150274
negative_passages.text: Inverse of a function - $f^-(x)$ in a restricted domain
negative_passages.docid: 18734
negative_passages.text: Showing that a function is differentiable
negative_passages.docid: 88559
negative_passages.text: Which function (s) is(are) the k-th derivative of itself?
negative_passages.docid: 3387
negative_passages.text: Derivative of $f(x)=|x|$
negative_passages.docid: 69378
negative_passages.text: The derivative of $x!$ and its continuity
negative_passages.docid: 52587
negative_passages.text: Real analysis : Problem related to inverse
negative_passages.docid: 134871
negative_passages.text: Using definition of derivative to differentiate $f(x)= \sqrt{x}+1$
negative_passages.docid: 4813
negative_passages.text: On finding polynomials that approximate a function and its derivative (extensions of Stone-Weierstrass?)
negative_passages.docid: 62067
negative_passages.text: Inverse function of $x^x$
negative_passages.docid: 45071
negative_passages.text: Having the derivative be an operator