{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{2}$}f\\left(a , \\mu , \\sigma , x\\right):=a\\,\\exp \\left(\\frac{-\\left(x-\\mu\\right)^2}{2\\,\\sigma^2}\\right)\\]"
      ],
      "text/plain": [
       "                                                         2\n",
       "                                               - (x - mu)\n",
       "(%o2)              f(a, mu, sigma, x) := a exp(-----------)\n",
       "                                                       2\n",
       "                                                2 sigma"
      ],
      "text/x-maxima": [
       "f(a,mu,sigma,x):=a*exp((-(x-mu)^2)/(2*sigma^2))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(a, mu, sigma, x) := a*exp(-(x-mu)^2/(2*sigma^2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{11}$}-\\frac{a\\,\\left(x-\\mu\\right)\\,e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }}{\\sigma^2}\\]"
      ],
      "text/plain": [
       "                                                   2\n",
       "                                           (x - mu)\n",
       "                                         - ---------\n",
       "                                                  2\n",
       "                                           2 sigma\n",
       "                            a (x - mu) %e\n",
       "(%o11)                    - ------------------------\n",
       "                                          2\n",
       "                                     sigma"
      ],
      "text/x-maxima": [
       "-(a*(x-mu)*%e^-((x-mu)^2/(2*sigma^2)))/sigma^2"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(f(a, mu, sigma, x), x);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{12}$}e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }\\]"
      ],
      "text/plain": [
       "                                             2\n",
       "                                     (x - mu)\n",
       "                                   - ---------\n",
       "                                            2\n",
       "                                     2 sigma\n",
       "(%o12)                           %e"
      ],
      "text/x-maxima": [
       "%e^-((x-mu)^2/(2*sigma^2))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(f(a, mu, sigma, x), a);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{13}$}\\frac{a\\,\\left(x-\\mu\\right)\\,e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }}{\\sigma^2}\\]"
      ],
      "text/plain": [
       "                                                  2\n",
       "                                          (x - mu)\n",
       "                                        - ---------\n",
       "                                                 2\n",
       "                                          2 sigma\n",
       "                           a (x - mu) %e\n",
       "(%o13)                     ------------------------\n",
       "                                         2\n",
       "                                    sigma"
      ],
      "text/x-maxima": [
       "(a*(x-mu)*%e^-((x-mu)^2/(2*sigma^2)))/sigma^2"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(f(a, mu, sigma, x), mu);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{14}$}\\frac{a\\,\\left(x-\\mu\\right)^2\\,e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }}{\\sigma^3}\\]"
      ],
      "text/plain": [
       "                                                   2\n",
       "                                           (x - mu)\n",
       "                                         - ---------\n",
       "                                                  2\n",
       "                                     2     2 sigma\n",
       "                           a (x - mu)  %e\n",
       "(%o14)                     -------------------------\n",
       "                                         3\n",
       "                                    sigma"
      ],
      "text/x-maxima": [
       "(a*(x-mu)^2*%e^-((x-mu)^2/(2*sigma^2)))/sigma^3"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(f(a, mu, sigma, x), sigma);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Maxima",
   "language": "maxima",
   "name": "maxima"
  },
  "language_info": {
   "codemirror_mode": "maxima",
   "file_extension": ".mac",
   "mimetype": "text/x-maxima",
   "name": "maxima",
   "pygments_lexer": "maxima",
   "version": "5.43.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}