query: How to show $\frac {\partial a^{T}X^{-1}b}{\partial X} = -\left( X^{-1}\right) ^{T}ab^{T}\left( X^{-1}\right) ^{T}$?
positive_passages.docid: 21553
positive_passages.text: Prove that $\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$
negative_passages.docid: 45742
negative_passages.text: Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
negative_passages.docid: 87303
negative_passages.text: Show that $\frac{a}{c} + \frac{b}{d} +\frac{c}{a} + \frac{d}{b}\le-12$
negative_passages.docid: 75604
negative_passages.text: Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
negative_passages.docid: 61782
negative_passages.text: How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
negative_passages.docid: 17769
negative_passages.text: Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$
negative_passages.docid: 57407
negative_passages.text: Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.
negative_passages.docid: 36437
negative_passages.text: How to show that $\log (\frac{2a}{1-a^2}+\frac{2b}{1-b^2}+\frac{2c}{1-c^2})= \log\frac{2a}{1-a^2}+ \log \frac{2b}{1-b^2}+ \log \frac{2c}{1-c^2}$
negative_passages.docid: 71708
negative_passages.text: Proving that $\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \lvert f(z) \rvert^2 = 4 \lvert f'(z) \rvert^2$
negative_passages.docid: 34398
negative_passages.text: Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$
negative_passages.docid: 135649
negative_passages.text: How is $\lim_{x \to a}\left(\frac{x^n - a^n}{x - a}\right) = n\times a^{n-1}$?
negative_passages.docid: 34702
negative_passages.text: Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
negative_passages.docid: 42805
negative_passages.text: Show that $\int\limits_0^1 \left(x^{x}\right)^{\left(x^{x}\right)^{\left(x^{x}\right)^{\left(x^{x}\right)^{⋰}}}}\ \mathrm{d}x=\frac{\pi^2}{12}$.
negative_passages.docid: 95774
negative_passages.text: $\frac{\partial^2 u}{\partial t^2}-c^2\frac{\partial^2u}{\partial x^2}=0\text{ implies } \frac{\partial^2 u}{\partial z \partial y}=0$
negative_passages.docid: 12726
negative_passages.text: Differentiating both sides of a non-differential equation
negative_passages.docid: 153089
negative_passages.text: How to find $\partial\chi^2/\partial a$ where $\chi^2=\sum_{i=1}^N\frac{D(x_i)-a-b(x_i)^2}{\sigma_i^2}$?
negative_passages.docid: 28416
negative_passages.text: Show that $\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$