diff --git a/CM20315_Gradients_I.ipynb b/CM20315_Gradients_I.ipynb
index e436851..6cfb237 100644
--- a/CM20315_Gradients_I.ipynb
+++ b/CM20315_Gradients_I.ipynb
@@ -4,7 +4,8 @@
   "metadata": {
     "colab": {
       "provenance": [],
-      "authorship_tag": "ABX9TyOVcqVtSrxHzifl2v6uaO71",
+      "collapsed_sections": [],
+      "authorship_tag": "ABX9TyMDEfAZvjcjpvBNmdrYv3EW",
       "include_colab_link": true
     },
     "kernelspec": {
@@ -46,7 +47,7 @@
         "Suppose that we know the current values of $\\beta_{0},\\beta_{1},\\beta_{2},\\beta_{3},\\beta_{4},\\omega_{0},\\omega_{1},\\omega_{2},\\omega_{3},\\omega_{4}$, and $x$. We could obviously calculate $y$.   But we also want to know how $y$ changes when we make a small change to $\\beta_{0},\\beta_{1},\\beta_{2},\\beta_{3},\\beta_{4},\\omega_{0},\\omega_{1},\\omega_{2},\\omega_{3}$, or $\\omega_{4}$.  In other words, we want to compute the ten derivatives:\n",
         "\n",
         "\\begin{eqnarray*}\n",
-        "\\frac{\\partial y}{\\partial \\beta_{0}}, \\quad \\frac{\\partial y}{\\partial \\beta_{1}}, \\quad \\frac{\\partial y}{\\partial \\beta_{2}}, \\quad \\frac{\\partial \\beta_{3}}{\\partial d}, \\quad\n",
+        "\\frac{\\partial y}{\\partial \\beta_{0}}, \\quad \\frac{\\partial y}{\\partial \\beta_{1}}, \\quad \\frac{\\partial y}{\\partial \\beta_{2}}, \\quad \\frac{\\partial y }{\\partial \\beta_{3}}, \\quad\n",
         "\\frac{\\partial y}{\\partial \\beta_{4}}, \\quad \\frac{\\partial y}{\\partial \\omega_{0}}, \\quad \\frac{\\partial y}{\\partial \\omega_{1}}, \\quad \\frac{\\partial y}{\\partial \\omega_{2}}, \\quad \\frac{\\partial y}{\\partial \\omega_{3}},  \\quad\\mbox{and} \\quad \\frac{\\partial y}{\\partial \\omega_{4}}.\n",
         "\\end{eqnarray*}"
       ],