diff --git a/doc/source/derivs/compderivs.ipynb b/doc/source/derivs/compderivs.ipynb
index 668b0d5b..5f19201f 100644
--- a/doc/source/derivs/compderivs.ipynb
+++ b/doc/source/derivs/compderivs.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "f751a5e0",
+   "id": "091504b8",
    "metadata": {},
    "source": [
     "# Composition derivatives\n",
@@ -40,7 +40,7 @@
   },
   {
    "cell_type": "raw",
-   "id": "59ede80a",
+   "id": "bc68ade8",
    "metadata": {
     "raw_mimetype": "text/restructuredtext"
    },
@@ -57,15 +57,12 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d46932aa",
+   "id": "e1ac0452",
    "metadata": {},
    "source": [
     "## xN (in)dependent\n",
     "\n",
-    "Let's suppose that some quantity $\\Upsilon$ depends on mole fractions. If all the mole fractions are considered to be independent, the total differential is obtained from\n",
-    "\n",
-    "$\\newcommand{\\deriv}[3]{\\left(\\frac{\\partial #1}{\\partial #2}\\right)_{#3}}$\n",
-    "\n",
+    "Let's suppose that some quantity $\\Upsilon$ depends on mole fractions. If all the mole fractions are considered to be independent, the total differential is obtained from $\\newcommand{\\deriv}[3]{\\left(\\frac{\\partial #1}{\\partial #2}\\right)_{#3}}$\n",
     "$$\n",
     "{\\rm d} \\Upsilon = \\sum_j\\deriv{\\Upsilon}{x_j}{x_{i\\neq j}} {\\rm d}x_j\n",
     "$$\n",
@@ -88,26 +85,15 @@
     "\\deriv{x_N}{x_i}{} = -1\n",
     "$$\n",
     "\n",
-    "So if the library (e.g., CoolProp and TREND) allows for the fractions to be independent, you can use the molar composition derivatives with the mole fractions treated as being indepenent to obtain derivatives with one of the mole fractions dependent on the other $N-1$ fractions."
+    "So if the library (e.g., CoolProp and TREND) allows for the fractions to be dependent (either option is allowed in CoolProp, TREND uses N-1 independent mole fractions), you can use the molar composition derivatives with the mole fractions treated as being independent to obtain derivatives with one of the mole fractions dependent on the other $N-1$ fractions."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
-   "id": "2ec44ccf",
+   "execution_count": null,
+   "id": "7cce6740",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'0.18.1.dev0'"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import teqp, numpy as np\n",
     "teqp.__version__"
@@ -115,26 +101,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "id": "53ba18fe",
+   "execution_count": null,
+   "id": "5869e1d6",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "-0.04358738425351122\n",
-      "-0.21188579988125827\n",
-      "-0.03650566667904926\n",
-      "-0.07488856488580686\n",
-      "-0.20693890096529247\n",
-      "0.014468933385218725\n",
-      "-0.005978809921279951\n",
-      "-0.0027918555000108207\n",
-      "0.0\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "j = {\n",
     "    'components': [\"Methane\", \"Nitrogen\", \"Oxygen\"],\n",
@@ -206,7 +176,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "594e48be",
+   "id": "b81e55cb",
    "metadata": {},
    "source": [
     "With CoolProp, version 6.6.0, the following script in C++:\n",