diff --git a/Rapport.ipynb b/Rapport.ipynb
index 06313e854b60ba0a693bb295fe993e1e1c0d7d9e..ebcc93899c84762cbc359fdd508439586c62f674 100644
--- a/Rapport.ipynb
+++ b/Rapport.ipynb
@@ -466,121 +466,118 @@
     "\n",
     "## Réseaux de Neurones Artificiels\n",
     "\n",
-    "$$Z^{L+1}=W^{L+1}A^{L}+B^{L+1}\\\\\n",
-    "A^{L+1}=\\sigma(Z^{L+1})$$\n",
+    "'''\n",
+    "\\begin{align*}\n",
+    "Z^{L+1}=W^{L+1}A^{L}+B^{L+1}\\\\\n",
+    "A^{L+1}=\\sigma(Z^{L+1})\n",
+    "\\end{align*}\n",
+    "'''\n",
     "\n",
-    "$$C = \\frac{1}{N_{out}}\\sum_{i=1}^{N_{out}} (\\hat{y_i} - y_i)^2$$\n",
+    "'''\n",
+    "\\begin{align*}\n",
+    "C = \\frac{1}{N_{out}}\\sum_{i=1}^{N_{out}} (\\hat{y_i} - y_i)^2\n",
+    "\\end{align*}\n",
+    "'''\n",
     "\n",
     "### 1\n",
     "\n",
-    "$$\\begin{align*}\n",
+    "'''\n",
+    "\\begin{align*}\n",
     "\\sigma(x)&=\\frac{1}{1+e^{-x}} \\\\\n",
     "\\Rightarrow \\sigma'(x)&=\\frac{-e^{-x}}{-(1+e^{-x})^2} \\\\\n",
     "\\Rightarrow \\sigma'(x)&=\\frac{1}{1+e^{-x}}(\\frac{1+e^{-x}-1}{1+e^{-x}}) \\\\\n",
     "\\Rightarrow \\sigma'(x)&=\\sigma(\\frac{1+e^{-x}}{1+e^{-x}}-\\frac{1}{1+e^{-x}}) \\\\\n",
     "\\Rightarrow \\sigma'(x)&=\\sigma(1-\\sigma)\n",
-    "\\end{align*}$$\n",
+    "\\end{align*}\n",
+    "'''\n",
     "\n",
     "### 2\n",
     "\n",
-    "$$\n",
+    "'''\n",
     "\\begin{align*}\n",
     "\\frac{\\partial C}{\\partial A^{(2)}} ? \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial a_i^{(2)}}&=\\frac{1}{N_{out}}\\sum_{i=1}^{N_{out}} (a_i^{(2)} - y_i)^2 \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial a_i^{(2)}}&=\\frac{2}{N_{out}} (a_i^{(2)} - y_i) \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial A^{(2)}}&=\\frac{2}{N_{out}} (A^{(2)} - Y)\n",
     "\\end{align*}\n",
-    "$$\n",
+    "'''\n",
     "\n",
     "### 3\n",
     "\n",
-    "$$\n",
+    "'''\n",
     "\\begin{align*}\n",
     "\\frac{\\partial C}{\\partial Z^{(2)}}&=\\frac{\\partial C}{\\partial A^{(2)}}\\frac{\\partial A^{(2)}}{\\partial Z^{(2)}} \\\\\n",
     "A^{(2)}&=\\sigma (Z^{(2)}) \\\\\n",
     "\\frac{\\partial A^{(2)}}{\\partial Z^{(2)}}&=A^{(2)}(1-A^{(2)}) \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial Z^{(2)}}&=\\frac{\\partial C}{\\partial A^{(2)}}[A^{(2)}(1-A^{(2)})]\n",
     "\\end{align*}\n",
-    "$$\n",
+    "'''\n",
     "\n",
     "### 4\n",
     "\n",
-    "$$\n",
+    "'''\n",
     "\\begin{align*}\n",
     "\\frac{\\partial C}{\\partial W^{(2)}}&=\\frac{\\partial C}{\\partial Z^{(2)}}\\frac{\\partial Z^{(2)}}{\\partial W^{(2)}} \\\\\n",
     "Z^{(2)}&=W^{(2)}A^{(1)}+B^{(2)} \\\\\n",
     "\\frac{\\partial Z^{(2)}}{\\partial W^{(2)}}&=A^{(1)} \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial W^{(2)}}&=\\frac{\\partial C}{\\partial Z^{(2)}}A^{(1)}\n",
     "\\end{align*}\n",
-    "$$\n",
+    "'''\n",
     "\n",
     "### 5\n",
     "\n",
-    "$$\n",
+    "'''\n",
     "\\begin{align*}\n",
     "\\frac{\\partial C}{\\partial B^{(2)}}&=\\frac{\\partial C}{\\partial Z^{(2)}}\\frac{\\partial Z^{(2)}}{\\partial B^{(2)}} \\\\\n",
     "Z^{(2)}&=W^{(2)}A^{(1)}+B^{(2)} \\\\\n",
     "\\frac{\\partial Z^{(2)}}{\\partial B^{(2)}}&=1 \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial B^{(2)}}&=\\frac{\\partial C}{\\partial Z^{(2)}}\n",
     "\\end{align*}\n",
-    "$$\n",
+    "'''\n",
     "\n",
     "### 6\n",
     "\n",
-    "$$\n",
+    "'''\n",
     "\\begin{align*}\n",
     "\\frac{\\partial C}{\\partial A^{(1)}}&=\\frac{\\partial C}{\\partial Z^{(2)}}\\frac{\\partial Z^{(2)}}{\\partial A^{(1)}} \\\\\n",
     "Z^{(2)}&=W^{(2)}A^{(1)}+B^{(2)} \\\\\n",
     "\\frac{\\partial Z^{(2)}}{\\partial A^{(1)}}&=W^{(2)} \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial A^{(1)}}&=\\frac{\\partial C}{\\partial Z^{(2)}}W^{(2)}\n",
     "\\end{align*}\n",
-    "$$\n",
+    "'''\n",
     "\n",
     "### 7\n",
     "\n",
-    "$$\n",
+    "'''\n",
     "\\begin{align*}\n",
     "\\frac{\\partial C}{\\partial Z^{(1)}}&=\\frac{\\partial C}{\\partial A^{(1)}}\\frac{\\partial A^{(1)}}{\\partial Z^{(1)}} \\\\\n",
     "A^{(1)}&=\\sigma (Z^{(1)}) \\\\\n",
     "\\frac{\\partial A^{(1)}}{\\partial Z^{(1)}}&=A^{(1)}(1-A^{(1)}) \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial Z^{(1)}}&=\\frac{\\partial C}{\\partial A^{(1)}}[A^{(1)}(1-A^{(1)})]\n",
     "\\end{align*}\n",
-    "$$\n",
+    "'''\n",
     "\n",
     "### 8\n",
     "\n",
-    "$$\n",
+    "'''\n",
     "\\begin{align*}\n",
     "\\frac{\\partial C}{\\partial W^{(1)}}&=\\frac{\\partial C}{\\partial Z^{(1)}}\\frac{\\partial Z^{(1)}}{\\partial W^{(1)}} \\\\\n",
     "Z^{(1)}&=W^{(1)}A^{(0)}+B^{(1)} \\\\\n",
     "\\frac{\\partial Z^{(1)}}{\\partial W^{(1)}}&=A^{(0)} \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial W^{(1)}}&=\\frac{\\partial C}{\\partial Z^{(1)}}A^{(0)}\n",
     "\\end{align*}\n",
-    "$$\n",
+    "'''\n",
     "\n",
     "### 9\n",
     "\n",
-    "$$\n",
+    "'''\n",
     "\\begin{align*}\n",
     "\\frac{\\partial C}{\\partial B^{(1)}}&=\\frac{\\partial C}{\\partial Z^{(1)}}\\frac{\\partial Z^{(1)}}{\\partial B^{(1)}} \\\\\n",
     "Z^{(1)}&=W^{(1)}A^{(0)}+B^{(1)} \\\\\n",
     "\\frac{\\partial Z^{(1)}}{\\partial B^{(1)}}&=1 \\\\\n",
     "\\Rightarrow \\frac{\\partial C}{\\partial B^{(1)}}&=\\frac{\\partial C}{\\partial Z^{(1)}}\n",
     "\\end{align*}\n",
-    "$$\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\\begin{align*}\n",
-    "\\sigma(x)&=\\frac{1}{1+e^{-x}} \\\\\n",
-    "\\Rightarrow \\sigma'(x)&=\\frac{-e^{-x}}{-(1+e^{-x})^2} \\\\\n",
-    "\\Rightarrow \\sigma'(x)&=\\frac{1}{1+e^{-x}}(\\frac{1+e^{-x}-1}{1+e^{-x}}) \\\\\n",
-    "\\Rightarrow \\sigma'(x)&=\\sigma(\\frac{1+e^{-x}}{1+e^{-x}}-\\frac{1}{1+e^{-x}}) \\\\\n",
-    "\\Rightarrow \\sigma'(x)&=\\sigma(1-\\sigma)\n",
-    "\\end{align*}$$"
+    "'''\n"
    ]
   },
   {