query: How does $\sigma’(x)$ simplify to $\sigma(x)(1-\sigma(x))$?
positive_passages.docid: 22916
positive_passages.text: Derivative of sigmoid function $\sigma (x) = \frac{1}{1+e^{-x}}$
negative_passages.docid: 141286
negative_passages.text: When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
negative_passages.docid: 7530
negative_passages.text: Why this $\sigma \pi \sigma^{-1}$ keeps appearing in my group theory book? (cycle decomposition)
negative_passages.docid: 148571
negative_passages.text: Simplify function notation
negative_passages.docid: 103307
negative_passages.text: Generate the smallest $\sigma$-algebra containing a given family of sets
negative_passages.docid: 138419
negative_passages.text: Sigma algebra and algebra difference
negative_passages.docid: 11319
negative_passages.text: Is $M=\{(x,|x|): x \in (-1, 1)\}$ not a differentiable manifold?
negative_passages.docid: 102398
negative_passages.text: Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative
negative_passages.docid: 132653
negative_passages.text: How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
negative_passages.docid: 121661
negative_passages.text: Evaluating the sum $\Sigma \, \frac{1}{k(k+p)}$
negative_passages.docid: 73869
negative_passages.text: $\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
negative_passages.docid: 56032
negative_passages.text: How come $\frac{1}{1-x}$ and $\frac{x}{1-x}$ have the same derivative?
negative_passages.docid: 147783
negative_passages.text: Showing a sigma algebra is the union of certain collection of sigma algebras
negative_passages.docid: 69715
negative_passages.text: Proving $\text{Var}{(\hat{y}_h)} = \sigma^2 \left(\frac{1}{n} + \frac{(x_h-\bar{x})^2}{S_{xx}}\right)$
negative_passages.docid: 10222
negative_passages.text: Simplify $\sum (x_i- \mu)^2$
negative_passages.docid: 156831
negative_passages.text: Prove $\Sigma_{k=0}^{n-1}\lfloor x+\frac{k}{n}\rfloor=\lfloor nx\rfloor$ , n is a Natural Number
negative_passages.docid: 19285
negative_passages.text: simplifying $ (h^2_2-h^2_3)\over ({1\over h_3})-({1\over h_2})$