Derivative of Sigmoid Function

DerivativeSigmoidFunction.ipynb

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    "### Derivative of Sigmoid Function\n",
    "- [シグモイド関数の微分](https://www.iwanttobeacat.com/entry/2018/07/18/195219)\n",
    "\n",
    "[分数関数の微分公式](https://gist.github.com/shotahorii/3ece437fefb60d978517bad8c86aea64)を使ってシグモイド関数の微分を計算する。"
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       "シグモイド関数は以下。\n",
       "<br><br>\n",
       "$$\\sigma(a) = \\frac{1}{1+exp(-a)}$$"
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    "%%latex\n",
    "シグモイド関数は以下。\n",
    "<br><br>\n",
    "$$\\sigma(a) = \\frac{1}{1+exp(-a)}$$"
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       "$$\\frac{d\\sigma(a)}{da} = \\frac{(1)'(1+exp(-a))-1(1+exp(-a))'}{(1+exp(-a))^2}$$<br>\n",
       "$$=\\frac{0-(-exp(-a))}{(1+exp(-a))^2}$$<br>\n",
       "$$=\\frac{1}{1+exp(-a)}\\frac{exp(-a)}{1+exp(-a)}$$<br>\n",
       "$$=\\sigma(a)\\frac{exp(-a)}{1+exp(-a)}$$<br>\n",
       "$$=\\sigma(a)\\frac{1+exp(-a)-1}{1+exp(-a)}$$<br>\n",
       "$$=\\sigma(a)(1-\\frac{1}{1+exp(-a)})$$<br>\n",
       "$$=\\sigma(a)(1-\\sigma(a))$$"
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    "%%latex\n",
    "$$\\frac{d\\sigma(a)}{da} = \\frac{(1)'(1+exp(-a))-1(1+exp(-a))'}{(1+exp(-a))^2}$$<br>\n",
    "$$=\\frac{0-(-exp(-a))}{(1+exp(-a))^2}$$<br>\n",
    "$$=\\frac{1}{1+exp(-a)}\\frac{exp(-a)}{1+exp(-a)}$$<br>\n",
    "$$=\\sigma(a)\\frac{exp(-a)}{1+exp(-a)}$$<br>\n",
    "$$=\\sigma(a)\\frac{1+exp(-a)-1}{1+exp(-a)}$$<br>\n",
    "$$=\\sigma(a)(1-\\frac{1}{1+exp(-a)})$$<br>\n",
    "$$=\\sigma(a)(1-\\sigma(a))$$"
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