diff --git a/Rapport.ipynb b/Rapport.ipynb index 4e3dc956fddc0e0b411ae857bd6fd745d325f8f2..06313e854b60ba0a693bb295fe993e1e1c0d7d9e 100644 --- a/Rapport.ipynb +++ b/Rapport.ipynb @@ -473,15 +473,13 @@ "\n", "### 1\n", "\n", - "$$\n", - "\\begin{align*}\n", + "$$\\begin{align*}\n", "\\sigma(x)&=\\frac{1}{1+e^{-x}} \\\\\n", "\\Rightarrow \\sigma'(x)&=\\frac{-e^{-x}}{-(1+e^{-x})^2} \\\\\n", "\\Rightarrow \\sigma'(x)&=\\frac{1}{1+e^{-x}}(\\frac{1+e^{-x}-1}{1+e^{-x}}) \\\\\n", "\\Rightarrow \\sigma'(x)&=\\sigma(\\frac{1+e^{-x}}{1+e^{-x}}-\\frac{1}{1+e^{-x}}) \\\\\n", "\\Rightarrow \\sigma'(x)&=\\sigma(1-\\sigma)\n", - "\\end{align*}\n", - "$$\n", + "\\end{align*}$$\n", "\n", "### 2\n", "\n", @@ -572,6 +570,19 @@ "$$\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\begin{align*}\n", + "\\sigma(x)&=\\frac{1}{1+e^{-x}} \\\\\n", + "\\Rightarrow \\sigma'(x)&=\\frac{-e^{-x}}{-(1+e^{-x})^2} \\\\\n", + "\\Rightarrow \\sigma'(x)&=\\frac{1}{1+e^{-x}}(\\frac{1+e^{-x}-1}{1+e^{-x}}) \\\\\n", + "\\Rightarrow \\sigma'(x)&=\\sigma(\\frac{1+e^{-x}}{1+e^{-x}}-\\frac{1}{1+e^{-x}}) \\\\\n", + "\\Rightarrow \\sigma'(x)&=\\sigma(1-\\sigma)\n", + "\\end{align*}$$" + ] + }, { "cell_type": "markdown", "metadata": {},