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   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/MeiraDavidson/math_module2/blob/main/notebooks/ch4_rules.ipynb)\n\n",
    "# Chapter 4 — Companion Notebook\n",
    "## A Toolkit for Slopes\n",
    "*How to differentiate almost anything without ever touching a difference quotient again*\n",
    "\n",
    "Three live pictures of the differentiation rules: a **drill** that names which rule a function calls for and shows the worked derivative, a growing rectangle that *proves* the product rule $(fg)'=f'g+fg'$ by watching its two strips, and a chain-rule machine that assembles $f'(g(x))\\cdot g'(x)$ one factor at a time.\n",
    "\n",
    "> **How to use this notebook.** Run every cell from the top (Shift+Enter). Each widget below is live — drag the sliders and watch the picture respond. Requires `ipywidgets` and `matplotlib`."
   ]
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   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "from ipywidgets import (interact, interactive, fixed, Dropdown, Checkbox,\n",
    "                        Button, Output, VBox, HBox,\n",
    "                        FloatSlider, IntSlider, FloatLogSlider)\n",
    "from IPython.display import HTML, display, Markdown\n",
    "\n",
    "# Book 2 palette — matches the printed figures in figures/png/\n",
    "BLUE=\"#1f4e79\"; RED=\"#c0392b\"; GREEN=\"#2e8b57\"; ORANGE=\"#e08e0b\"\n",
    "PURPLE=\"#6c3483\"; TEAL=\"#1b9e9e\"; GRAY=\"#7f8c8d\"; DARK=\"#2c3e50\"\n",
    "SHADE=\"#9fc5e8\"; SHADE2=\"#f4b6ad\"; SHADEG=\"#a9dfbf\"; LIGHT=\"#d6dbdf\"\n",
    "\n",
    "plt.rcParams.update({\n",
    "    \"figure.figsize\": (7.2, 4.5), \"figure.dpi\": 96,\n",
    "    \"font.family\": \"serif\", \"mathtext.fontset\": \"cm\", \"font.size\": 12,\n",
    "    \"axes.spines.top\": False, \"axes.spines.right\": False,\n",
    "    \"axes.grid\": True, \"grid.color\": LIGHT, \"grid.linewidth\": 0.7,\n",
    "    \"lines.linewidth\": 2.2, \"lines.solid_capstyle\": \"round\",\n",
    "})\n",
    "\n",
    "def axes(ax=None, title=None):\n",
    "    '''A clean axes with a light grid; returns the axes.'''\n",
    "    if ax is None:\n",
    "        _, ax = plt.subplots()\n",
    "    if title:\n",
    "        ax.set_title(title, color=DARK)\n",
    "    return ax\n"
   ]
  },
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   "cell_type": "markdown",
   "id": "3a88442a",
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    "## 1. Rule detector\n",
    "\n",
    "Before you can *use* the rules you have to **see** which one a function is asking for. Pick a function from the dropdown; the blue curve is $f$ and the red curve is its derivative $f'$ (computed by hand, plotted for a reality check). Then tick **reveal** to name the rule(s) at work and read off the worked derivative.\n",
    "\n",
    "The whole game of this chapter is pattern recognition: a *power* ($x^5$), a *product* (two factors multiplied, $x^2\\sin x$), a *quotient* (one thing over another, $\\tfrac{x}{x^2+1}$), or a *composition* — a function tucked **inside** another, $(x^2+1)^7$ or $\\sin 3x$ — which is the chain rule's territory."
   ]
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     "output_type": "display_data",
     "data": {
      "text/plain": [
       "interactive(children=(Dropdown(description='function', options=('x^5', 'x^2 * sin(x)', '(x^2 + 1)^7', 'x / (x^…"
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    "# Each preset carries its f, its hand-computed f', the rule name,\n",
    "# and the worked steps (LaTeX) revealed on demand.\n",
    "_PRESETS = {\n",
    "    'x^5':\n",
    "        dict(f=lambda x: x**5, df=lambda x: 5*x**4,\n",
    "             rule='Power rule',\n",
    "             work=r'$\\frac{d}{dx}x^5 = 5x^{5-1} = 5x^4$',\n",
    "             note='Bring the exponent down, subtract one.'),\n",
    "    'x^2 * sin(x)':\n",
    "        dict(f=lambda x: x**2*np.sin(x),\n",
    "             df=lambda x: 2*x*np.sin(x) + x**2*np.cos(x),\n",
    "             rule='Product rule',\n",
    "             work=(r'$\\frac{d}{dx}\\big[x^2\\sin x\\big]'\n",
    "                   r'=(2x)\\sin x + x^2(\\cos x)$'),\n",
    "             note=\"first' \\u00b7 second + first \\u00b7 second'.\"),\n",
    "    '(x^2 + 1)^7':\n",
    "        dict(f=lambda x: (x**2 + 1)**7,\n",
    "             df=lambda x: 7*(x**2 + 1)**6 * 2*x,\n",
    "             rule='Chain rule',\n",
    "             work=(r'$\\frac{d}{dx}(x^2+1)^7'\n",
    "                   r'=7(x^2+1)^6\\cdot 2x = 14x(x^2+1)^6$'),\n",
    "             note='Outer (power) first, leave the inside alone, '\n",
    "                  'times the inside derivative.'),\n",
    "    'x / (x^2 + 1)':\n",
    "        dict(f=lambda x: x/(x**2 + 1),\n",
    "             df=lambda x: (1 - x**2)/(x**2 + 1)**2,\n",
    "             rule='Quotient rule',\n",
    "             work=(r'$\\frac{d}{dx}\\frac{x}{x^2+1}'\n",
    "                   r'=\\frac{(1)(x^2+1)-(x)(2x)}{(x^2+1)^2}'\n",
    "                   r'=\\frac{1-x^2}{(x^2+1)^2}$'),\n",
    "             note='Bottom \\u00b7 top\\u2032 \\u2212 top \\u00b7 '\n",
    "                  'bottom\\u2032, all over bottom squared.'),\n",
    "    'e^x * x':\n",
    "        dict(f=lambda x: np.exp(x)*x,\n",
    "             df=lambda x: np.exp(x)*x + np.exp(x),\n",
    "             rule='Product rule (with $e^x$)',\n",
    "             work=(r'$\\frac{d}{dx}\\big[e^x x\\big]'\n",
    "                   r'=e^x\\cdot x + e^x\\cdot 1 = e^x(x+1)$'),\n",
    "             note='$e^x$ is its own derivative; the rest is the '\n",
    "                  'product rule.'),\n",
    "    'sin(3x)':\n",
    "        dict(f=lambda x: np.sin(3*x),\n",
    "             df=lambda x: 3*np.cos(3*x),\n",
    "             rule='Chain rule',\n",
    "             work=(r'$\\frac{d}{dx}\\sin(3x)'\n",
    "                   r'=\\cos(3x)\\cdot 3 = 3\\cos(3x)$'),\n",
    "             note='Outer (sine) first, times the inside '\n",
    "                  'derivative $3$.'),\n",
    "}\n",
    "\n",
    "def _detector(which='x^5', reveal=False):\n",
    "    p = _PRESETS[which]\n",
    "    # Keep windows where each function is well-behaved on screen.\n",
    "    hw = 1.6 if which == '(x^2 + 1)^7' else 3.0\n",
    "    xs = np.linspace(-hw, hw, 600)\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(xs, p['f'](xs), color=BLUE, lw=2.4, label=r'$f$')\n",
    "    ax.plot(xs, p['df'](xs), color=RED, lw=2.0, ls='--',\n",
    "            label=r\"$f'$\")\n",
    "    ax.axhline(0, color=GRAY, lw=0.8)\n",
    "    ax.set_xlim(-hw, hw)\n",
    "    ax.set_xlabel('$x$'); ax.set_ylabel('$y$')\n",
    "    ax.set_title(f'$f(x) = $ {which}', color=DARK)\n",
    "    ax.legend(loc='upper left', framealpha=0.9)\n",
    "    plt.show()\n",
    "    if reveal:\n",
    "        display(Markdown(f\"**Rule:** {p['rule']}\"))\n",
    "        display(Markdown(p['work']))\n",
    "        display(Markdown(f\"*{p['note']}*\"))\n",
    "    else:\n",
    "        display(Markdown('*Tick **reveal** to name the rule and '\n",
    "                         'see the worked derivative.*'))\n",
    "\n",
    "interact(_detector,\n",
    "         which=Dropdown(options=list(_PRESETS), value='x^5',\n",
    "                        description='function'),\n",
    "         reveal=Checkbox(value=False, description='reveal answer'));\n"
   ]
  },
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   "cell_type": "markdown",
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    "id": "8b898500"
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   "source": [
    "## 2. Why the product rule has *two* terms\n",
    "\n",
    "The naive guess $(fg)' = f'g'$ is wrong, and a growing rectangle shows exactly what it misses. Let the width be $f(t)=1+t$ and the height be $g(t)=1+0.6t$, so the **area** is the product $A(t)=f(t)\\,g(t)$. Watch the rectangle grow as $t$ advances.\n",
    "\n",
    "Each frame the area gains three pieces: a **blue** strip from the extra width ($f'\\,g$), a **green** strip from the extra height ($f\\,g'$), and a tiny **red** corner where both grew at once ($f'g'\\,\\Delta t$). As the step shrinks that corner vanishes faster than the strips — which is precisely why\n",
    "\n",
    "$$\\frac{d}{dt}(fg) = f'\\,g + f\\,g'.$$\n",
    "\n",
    "Two strips survive; the corner does not."
   ]
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       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
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       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
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       "    this.slider_id = slider_id;\n",
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       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
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       "\n",
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       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
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       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
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       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
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       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
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       "\n",
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       "    if(this.direction > 0){this.play_animation();}\n",
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       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
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       "      var loop_state = this.get_loop_state();\n",
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       "        this.last_frame();\n",
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       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
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       ".anim-state label {\n",
       "    margin-right: 8px;\n",
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       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
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       "  <div class=\"anim-controls\">\n",
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       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim4079cf76fc2241269c8f6cf0c2787cd0.play_animation()\">\n",
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       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img4079cf76fc2241269c8f6cf0c2787cd0\";\n",
       "    var slider_id = \"_anim_slider4079cf76fc2241269c8f6cf0c2787cd0\";\n",
       "    var loop_select_id = \"_anim_loop_select4079cf76fc2241269c8f6cf0c2787cd0\";\n",
       "    var frames = new Array(48);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAArIAAAGwCAYAAABVWYYWAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "AABJRU5ErkJggg==\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim4079cf76fc2241269c8f6cf0c2787cd0 = new Animation(frames, img_id, slider_id, 90.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ]
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "f = lambda t: 1 + t          # width\n",
    "g = lambda t: 1 + 0.6*t      # height\n",
    "fp, gp = 1.0, 0.6            # f'(t), g'(t) are constant here\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "_T = np.linspace(0.0, 2.0, 48)   # one t per frame\n",
    "_dt = 0.55                       # visible growth step per frame\n",
    "\n",
    "def _frame(i):\n",
    "    ax.clear()\n",
    "    t = _T[i]\n",
    "    w, h = f(t), g(t)\n",
    "    dw, dh = fp*_dt, gp*_dt\n",
    "    # Base rectangle: the current area f(t) g(t).\n",
    "    ax.add_patch(plt.Rectangle((0, 0), w, h, facecolor=LIGHT,\n",
    "                 edgecolor=DARK, lw=1.5, zorder=1))\n",
    "    ax.text(w/2, h/2, r'$f\\,g$', ha='center', va='center',\n",
    "            color=DARK, fontsize=14)\n",
    "    # Strip from extra width: f' g.\n",
    "    ax.add_patch(plt.Rectangle((w, 0), dw, h, facecolor=SHADE,\n",
    "                 edgecolor=BLUE, lw=1.2, alpha=0.85, zorder=2))\n",
    "    ax.text(w + dw/2, h/2, r\"$f'g$\", ha='center', va='center',\n",
    "            color=BLUE, fontsize=12, rotation=90)\n",
    "    # Strip from extra height: f g'.\n",
    "    ax.add_patch(plt.Rectangle((0, h), w, dh, facecolor=SHADEG,\n",
    "                 edgecolor=GREEN, lw=1.2, alpha=0.85, zorder=2))\n",
    "    ax.text(w/2, h + dh/2, r\"$fg'$\", ha='center', va='center',\n",
    "            color=GREEN, fontsize=12)\n",
    "    # The vanishing corner: f' g' (dt)^2.\n",
    "    ax.add_patch(plt.Rectangle((w, h), dw, dh, facecolor=SHADE2,\n",
    "                 edgecolor=RED, lw=1.2, zorder=3))\n",
    "    ax.annotate(r\"$f'g'$ (vanishes)\", xy=(w + dw/2, h + dh/2),\n",
    "                xytext=(w + dw/2 + 0.35, h + dh/2 + 0.7),\n",
    "                color=RED, fontsize=11,\n",
    "                arrowprops=dict(arrowstyle='->', color=RED))\n",
    "    ax.set_xlim(0, 5.0); ax.set_ylim(0, 4.0)\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_xlabel(r'width $f(t)=1+t$')\n",
    "    ax.set_ylabel(r'height $g(t)=1+0.6t$')\n",
    "    ax.set_title(f'$t = {t:.2f}$:   area $f g = {w*h:.2f}$',\n",
    "                 color=DARK)\n",
    "\n",
    "ani = animation.FuncAnimation(fig, _frame, frames=48, interval=90)\n",
    "plt.close(fig)\n",
    "HTML(ani.to_jshtml())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d06777f3",
   "metadata": {
    "id": "d06777f3"
   },
   "source": [
    "## 3. Build a derivative (the chain rule)\n",
    "\n",
    "Most real functions are **compositions** — an *outer* function wrapped around an *inner* one, $f(g(x))$. Pick an outer and an inner from the dropdowns; the notebook forms the composition $f(g(x))$ and assembles its derivative the way the chain rule tells you to:\n",
    "\n",
    "$$\\frac{d}{dx}\\,f(g(x)) = \\underbrace{f'(g(x))}_{\\text{outer}'\\text{ at the inside}}\\cdot\\;\\underbrace{g'(x)}_{\\text{inside}'}.$$\n",
    "\n",
    "Differentiate the outer, **leave the inside alone**, then multiply by the derivative of the inside. The blue curve is the composition $f(g(x))$; the red dashed curve is the derivative the rule produced — so you can confirm the assembled factors are right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d6c4bfae",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 604,
     "referenced_widgets": [
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      "e8eee797ba93410a9fce455ac6cd37d6"
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    "id": "d6c4bfae",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1782335558411,
     "user_tz": 240,
     "elapsed": 236,
     "user": {
      "displayName": "Meira Davidson",
      "userId": "09448014842742744623"
     }
    },
    "outputId": "a129ae7e-a7a9-4a25-b7bf-2f30d8665278"
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "interactive(children=(Dropdown(description='outer  $f$', options=('sin', 'exp', '(.)^3', 'sqrt'), value='sin')…"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "f1b04d5353b649c7b5224676b2f6e6cd"
      }
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Outer functions: f, f', and a LaTeX template g(.) -> f(.) and f'(.).\n",
    "_OUTER = {\n",
    "    'sin':   dict(f=np.sin, df=np.cos,\n",
    "                  f_tex=lambda u: rf'\\sin\\!\\left({u}\\right)',\n",
    "                  df_tex=lambda u: rf'\\cos\\!\\left({u}\\right)'),\n",
    "    'exp':   dict(f=np.exp, df=np.exp,\n",
    "                  f_tex=lambda u: rf'e^{{{u}}}',\n",
    "                  df_tex=lambda u: rf'e^{{{u}}}'),\n",
    "    '(.)^3': dict(f=lambda u: u**3, df=lambda u: 3*u**2,\n",
    "                  f_tex=lambda u: rf'\\left({u}\\right)^3',\n",
    "                  df_tex=lambda u: rf'3\\left({u}\\right)^2'),\n",
    "    'sqrt':  dict(f=np.sqrt, df=lambda u: 0.5/np.sqrt(u),\n",
    "                  f_tex=lambda u: rf'\\sqrt{{{u}}}',\n",
    "                  df_tex=lambda u: rf'\\frac{{1}}{{2\\sqrt{{{u}}}}}'),\n",
    "}\n",
    "# Inner functions: g, g', a LaTeX string, and a domain that keeps\n",
    "# sqrt's argument >= 0 so every composition is real on screen.\n",
    "_INNER = {\n",
    "    'x^2':    dict(g=lambda x: x**2, dg=lambda x: 2*x,\n",
    "                   tex='x^2', dtex='2x', dom=(-2.2, 2.2)),\n",
    "    '3x + 1': dict(g=lambda x: 3*x + 1, dg=lambda x: 3 + 0*x,\n",
    "                   tex='3x+1', dtex='3', dom=(0.0, 2.0)),\n",
    "    'x^2 + 1':dict(g=lambda x: x**2 + 1, dg=lambda x: 2*x,\n",
    "                   tex='x^2+1', dtex='2x', dom=(-2.2, 2.2)),\n",
    "}\n",
    "\n",
    "def _build(outer='sin', inner='x^2'):\n",
    "    o, n = _OUTER[outer], _INNER[inner]\n",
    "    a, b = n['dom']\n",
    "    xs = np.linspace(a, b, 600)\n",
    "    gx = n['g'](xs)\n",
    "    comp = o['f'](gx)                       # f(g(x))\n",
    "    deriv = o['df'](gx) * n['dg'](xs)       # f'(g(x)) * g'(x)\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(xs, comp, color=BLUE, lw=2.4, label=r'$f(g(x))$')\n",
    "    ax.plot(xs, deriv, color=RED, lw=2.0, ls='--',\n",
    "            label=r\"$f'(g(x))\\,g'(x)$\")\n",
    "    ax.axhline(0, color=GRAY, lw=0.8)\n",
    "    ax.set_xlim(a, b)\n",
    "    ax.set_xlabel('$x$'); ax.set_ylabel('$y$')\n",
    "    ax.set_title('Composition and its chain-rule derivative',\n",
    "                 color=DARK)\n",
    "    ax.legend(loc='upper left', framealpha=0.9)\n",
    "    plt.show()\n",
    "\n",
    "    # Assemble the answer factor by factor.\n",
    "    f_of_g = o['f_tex'](n['tex'])\n",
    "    outer_prime = o['df_tex'](n['tex'])\n",
    "    display(Markdown(rf\"**Composition:**  $f(g(x)) = {f_of_g}$\"))\n",
    "    display(Markdown(\n",
    "        r'**Chain rule:** $\\;\\dfrac{d}{dx}f(g(x))'\n",
    "        rf'= \\underbrace{{{outer_prime}}}_{{\\text{{outer}}\\,'\n",
    "        rf\"' \\text{{ at the inside}}}}\"\n",
    "        rf'\\;\\cdot\\;\\underbrace{{{n[\"dtex\"]}}}'\n",
    "        r\"_{\\text{inside}\\,'}$\"))\n",
    "\n",
    "interact(_build,\n",
    "         outer=Dropdown(options=list(_OUTER), value='sin',\n",
    "                        description='outer  $f$'),\n",
    "         inner=Dropdown(options=list(_INNER), value='x^2',\n",
    "                        description='inner  $g$'));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d1945ff",
   "metadata": {
    "id": "0d1945ff"
   },
   "source": [
    "---\n",
    "\n",
    "*Five rules — power, sum, product, quotient, chain — and you can now differentiate almost anything in seconds, never returning to a difference quotient. The chain rule is the one to keep closest: in Chapter 9 it becomes the engine of gradient descent, and run **backward** across a deep composition it is the backpropagation that trains every neural network.*"
   ]
  }
 ],
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       "IPY_MODEL_fb27bee5fd764a3ca95b5c686648736e",
       "IPY_MODEL_2f1b5e00663b49a7a6d6b12394135260",
       "IPY_MODEL_91cc765bb415445786195df2648e7016"
      ],
      "layout": "IPY_MODEL_3faa966a4c134d5685ab8339b331baf0"
     }
    },
    "fb27bee5fd764a3ca95b5c686648736e": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "DropdownModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "DropdownModel",
      "_options_labels": [
       "x^5",
       "x^2 * sin(x)",
       "(x^2 + 1)^7",
       "x / (x^2 + 1)",
       "e^x * x",
       "sin(3x)"
      ],
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "DropdownView",
      "description": "function",
      "description_tooltip": null,
      "disabled": false,
      "index": 3,
      "layout": "IPY_MODEL_f289cb8c2cdd4c58a79ef80897238c88",
      "style": "IPY_MODEL_140f84af069342539763f4ac52cb9856"
     }
    },
    "2f1b5e00663b49a7a6d6b12394135260": {
     "model_module": "@jupyter-widgets/controls",
     "model_name": "CheckboxModel",
     "model_module_version": "1.5.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "CheckboxModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "CheckboxView",
      "description": "reveal answer",
      "description_tooltip": null,
      "disabled": false,
      "indent": true,
      "layout": "IPY_MODEL_c1dfe7fc287e4f7f954207d15b53f4f6",
      "style": "IPY_MODEL_325c41e901d445d0a2c4b87a6ed8fb94",
      "value": false
     }
    },
    "91cc765bb415445786195df2648e7016": {
     "model_module": "@jupyter-widgets/output",
     "model_name": "OutputModel",
     "model_module_version": "1.0.0",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/output",
      "_model_module_version": "1.0.0",
      "_model_name": "OutputModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/output",
      "_view_module_version": "1.0.0",
      "_view_name": "OutputView",
      "layout": "IPY_MODEL_ba0a3e703b624fc69307c80278949b72",
      "msg_id": "",
      "outputs": [
       {
        "output_type": "display_data",
        "data": {
         "text/plain": "<Figure size 691.2x432 with 1 Axes>",
         "image/png": 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\n"
        },
        "metadata": {}
       },
       {
        "output_type": "display_data",
        "data": {
         "text/plain": "<IPython.core.display.Markdown object>",
         "text/markdown": "*Tick **reveal** to name the rule and see the worked derivative.*"
        },
        "metadata": {}
       }
      ]
     }
    },
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\n"
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        "data": {
         "text/plain": "<IPython.core.display.Markdown object>",
         "text/markdown": "**Composition:**  $f(g(x)) = \\sqrt{3x+1}$"
        },
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       },
       {
        "output_type": "display_data",
        "data": {
         "text/plain": "<IPython.core.display.Markdown object>",
         "text/markdown": "**Chain rule:** $\\;\\dfrac{d}{dx}f(g(x))= \\underbrace{\\frac{1}{2\\sqrt{3x+1}}}_{\\text{outer}\\,' \\text{ at the inside}}\\;\\cdot\\;\\underbrace{3}_{\\text{inside}\\,'}$"
        },
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       }
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