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": {},