query: On an algebra $F[x]$, defining operators $T,D$ as integration, differentiation, respectively, show that $DT = I$
positive_passages.docid: 29470
positive_passages.text: Problem involving Derivative and Antiderivative operators in Hoffman and Kunze's Linear Algebra
negative_passages.docid: 48524
negative_passages.text: Existence proof of the tensor product using the Adjoint functor theorem.
negative_passages.docid: 40549
negative_passages.text: How to proof the the derivative of $x^2$ is $2x$?
negative_passages.docid: 101267
negative_passages.text: Show: $\int f\, d\mu=\int\limits_0^{\infty}\mu(\left\{x\in X: f(x)>t\right\})\, dt$
negative_passages.docid: 144323
negative_passages.text: Differentiation of a function
negative_passages.docid: 153794
negative_passages.text: What is the meaning of $1/(D+a)$, where $D$ is the derivative operator?
negative_passages.docid: 117978
negative_passages.text: differentiation using formal definition i.e. $(x+h)$
negative_passages.docid: 13020
negative_passages.text: Proof for the funky trace derivative : $d (\operatorname{trace} (ABA'C))$?
negative_passages.docid: 109561
negative_passages.text: Find $F'(x)$ if $F(x) = \displaystyle \int_{0}^x xf(t)dt$.
negative_passages.docid: 130253
negative_passages.text: Differentiating $\mbox{tr} (ABA^TC)$ w.r.t. $A$
negative_passages.docid: 27705
negative_passages.text: Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$
negative_passages.docid: 71437
negative_passages.text: How is the derivative of $\textrm{Trace}\left\{ X^T A X B\right\}$ with respect to $X$ equal to $AXB + A^TXB^T$?
negative_passages.docid: 36826
negative_passages.text: Products of Differential Operators
negative_passages.docid: 118929
negative_passages.text: Why is integration the inverse of differentiation
negative_passages.docid: 33196
negative_passages.text: show that A(T) is a group under operation of composition of functions
negative_passages.docid: 62110
negative_passages.text: Proving a function $\frac{1}{2y}\int_{x-y}^{x+y} f(t) dt=f(x)$ is a linear polynomial
negative_passages.docid: 27812
negative_passages.text: Understanding the differential $dx$ when doing $u$-substitution