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{
"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": {},
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}
],
"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"
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"metadata": {},
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],
"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} }\\]"
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" 2\n",
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"%e^-((x-mu)^2/(2*sigma^2))"
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"execution_count": 15,
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"source": [
"diff(f(a, mu, sigma, x), a);"
]
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{
"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}\\]"
],
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" 2\n",
" (x - mu)\n",
" - ---------\n",
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" 2 sigma\n",
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" 2\n",
" sigma"
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"text/x-maxima": [
"(a*(x-mu)*%e^-((x-mu)^2/(2*sigma^2)))/sigma^2"
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"metadata": {},
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],
"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);"
]
}
],
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"name": "maxima"
},
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