diff --git a/is/UB3/ExerciseSheet3final.ipynb b/is/UB3/ExerciseSheet3final.ipynb
index eb11ca5..982e5b0 100644
--- a/is/UB3/ExerciseSheet3final.ipynb
+++ b/is/UB3/ExerciseSheet3final.ipynb
@@ -77,6 +77,27 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "$\\left(2\\pi\\right)^{-\\frac{k}{2}}\\left|\\Sigma\\right|^{-\\frac{1}{2}}\\cdot e^{-\\frac{1}{2}\\left(\\vec y-\\mu\\right)^T\\Sigma^{-1}\\left(\\vec y-\\mu\\right)}\\text{, where: }k=n\\text{ number of measurments},\\ \\Sigma=\\sigma I,\\ \\mu=X\\vec w$\n",
+    "\\begin{align*}\n",
+    "    &\\frac{d}{d\\vec w} \\left(2\\pi\\right)^{-\\frac{k}{2}}\\left|\\Sigma\\right|^{-\\frac{1}{2}}\\cdot e^{-\\frac{1}{2}\\left(\\vec y-\\mu\\right)^T\\Sigma^{-1}\\left(\\vec y-\\mu\\right)}\\\\ &=\\underbrace{\\left(2\\pi\\right)^{-\\frac{k}{2}}\\left|\\Sigma\\right|^{-\\frac{1}{2}}\\cdot e^{-\\frac{1}{2}\\left(\\vec y-\\mu\\right)^T\\Sigma^{-1}\\left(\\vec y-\\mu\\right)}}_{>0}\\frac{d}{d\\vec w}\\left(-\\frac{1}{2}\\left(\\vec y-\\mu\\right)^T\\Sigma^{-1}\\left(\\vec y-\\mu\\right)\\right)&\\overset{!}{=}&0\\\\\n",
+    "   \\Leftrightarrow &\\frac{d}{d\\vec w}-\\frac{1}{2}\\left(\\vec{y}-\\mu\\right)^T\\Sigma^{-1}\\left(\\vec{y}-\\mu\\right) &=&0\\\\\n",
+    "   \\Leftrightarrow & \\frac{d}{d\\vec w}\\left(\\vec{y}-\\mu\\right)^T\\Sigma^{-1}\\left(\\vec{y}-\\mu\\right) &=&0\\ (\\Sigma\\not=\\mathcal{O})\\\\\n",
+    "   \\Leftrightarrow & \\frac{d}{d\\vec w}\\left(\\vec{y}-\\mu\\right)^T\\left(\\vec{y}-\\mu\\right) &=&0\\\\\n",
+    "   \\Leftrightarrow & \\frac{d}{d\\vec w}\\left(\\left(\\vec{y}-X\\vec{w}\\right)^T\\right)\\left(\\vec{y}-X\\vec{w}\\right) + \\left(\\vec{y}-X\\vec{w}\\right)^T\\frac{d}{d\\vec w}\\left(\\vec{y}-X\\vec{w}\\right)&=&0\\\\\n",
+    "   \\Leftrightarrow & -X\\left(\\vec{y}-X\\vec{w}\\right)-\\left(\\vec{y}-X\\vec{w}\\right)^TX^T &=&0\\\\\n",
+    "   \\Leftrightarrow & -X\\left(\\vec{y}-X\\vec{w}\\right)-X\\left(\\vec{y}-X\\vec{w}\\right)&=&0\\\\\n",
+    "   \\Leftrightarrow & X\\left(\\vec{y}-X\\vec{w}\\right) &=&0\\\\\n",
+    "   \\Leftrightarrow & \\vec{y}-X\\vec{w} &=&0\\\\\n",
+    "   \\Leftrightarrow & \\vec{y}&=& X\\vec{w}\\\\\n",
+    "   \\Leftrightarrow & X^T\\vec{y} &=& X^TX\\vec{w}\\\\\n",
+    "   \\Leftrightarrow & \\vec{w} &=& \\left(X^TX\\right)^{-1}X^T\\vec{y}\\hspace{1cm} q.e.d.\n",
+    "\\end{align*}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "#  Linear regression (50 Points)\n",
     "\n",
     "In this exercise you will perform a regression analysis on a toy dataset. You will implement ridge regression and learn how to find a good model through a comparative performance analysis.\n",
diff --git a/is/UB3/ExerciseSheet3final.pdf b/is/UB3/ExerciseSheet3final.pdf
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--- /dev/null
+++ b/is/UB3/ExerciseSheet3final.pdf
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