{
	"cells" : 
	[
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "\\algorithm{product_rule}{Apply the Leibnitz rule to a derivative of a product}\n\nApply the product rule or ``Leibnitz\n  identity'' to an object which has the \\prop{Derivative} property, i.e."
				}
			],
			"hidden" : true,
			"source" : "\\algorithm{product_rule}{Apply the Leibnitz rule to a derivative of a product}\n\nApply the product rule or ``Leibnitz\n  identity'' to an object which has the \\prop{Derivative} property, i.e."
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}\\text{Attached property Derivative to~}D{\\#}.\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}D\\left(f g\\right)\\end{dmath*}"
				},
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}D{f} g+f D{g}\\end{dmath*}"
				}
			],
			"source" : "D{#}::Derivative;\nex:=D(f g);\nproduct_rule(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "latex",
			"cells" : 
			[
				{
					"cell_origin" : "client",
					"cell_type" : "latex_view",
					"source" : "This of course also works for derivatives which explicitly mention\nindices or components, as well as for multiple derivatives, as in the example below."
				}
			],
			"hidden" : true,
			"source" : "This of course also works for derivatives which explicitly mention\nindices or components, as well as for multiple derivatives, as in the example below."
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}D_{m n}\\left(f g\\right)\\end{dmath*}"
				}
			],
			"source" : "D{#}::Derivative.\nex:=D_{m n}(f g);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}D_{m}\\left(D_{n}{f} g+f D_{n}{g}\\right)\\end{dmath*}"
				}
			],
			"source" : "product_rule(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}D_{m}\\left(D_{n}{f} g\\right)+D_{m}\\left(f D_{n}{g}\\right)\\end{dmath*}"
				}
			],
			"source" : "distribute(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"cells" : 
			[
				{
					"cell_origin" : "server",
					"cell_type" : "latex_view",
					"source" : "\\begin{dmath*}{}D_{m}{D_{n}{f}} g+D_{n}{f} D_{m}{g}+D_{m}{f} D_{n}{g}+f D_{m}{D_{n}{g}}\\end{dmath*}"
				}
			],
			"source" : "product_rule(_);"
		},
		{
			"cell_origin" : "client",
			"cell_type" : "input",
			"source" : ""
		}
	],
	"description" : "Cadabra JSON notebook format",
	"version" : 1
}