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"categories": [
{
"id": "core",
"name": "Core Concepts"
},
{
"id": "calculus",
"name": "Calculus Topics"
}
],
"symbols": [
{
"id": "lim",
"symbol": "lim",
"name": "Limit operator",
"meaning": "Describes the value a function approaches."
},
{
"id": "integral",
"symbol": "∫",
"name": "Integral operator",
"meaning": "Represents accumulation and area."
}
],
"formulas": [
{
"id": "power_rule",
"name": "Power Rule",
"plain": "d/dx (x^n) = n*x^(n-1)",
"latex": "\\frac{d}{dx}x^n = nx^{n-1}",
"tags": [
"derivatives"
]
}
],
"topics": [
{
"id": "topic-template-derivative",
"category": "calculus",
"title": "Derivative Workflow Template",
"summary": "Template entry showing how a concept page is structured.",
"narrative": "Use this section for the plain-language teaching narrative. Explain what a derivative means, when to use it, and why the rule works.",
"symbols": [
"lim"
],
"formulas": [
"power_rule"
],
"examples": [
{
"id": "example-template-1",
"title": "Example Template",
"problem": "d/dx (x^3)",
"steps": [
{
"title": "Identify rule",
"explanation": "Use the power rule because the function is x raised to a power.",
"math": "d/dx (x^3)"
},
{
"title": "Apply rule",
"explanation": "Bring exponent down and subtract one from exponent.",
"math": "3x^2"
}
]
}
],
"related": [
"topic-template-limit"
]
},
{
"id": "topic-template-limit",
"category": "core",
"title": "Limit Workflow Template",
"summary": "Template entry for linked-topic navigation.",
"narrative": "Use this section to explain limit intuition, one-sided limits, and infinity behavior in plain language.",
"symbols": [
"lim"
],
"formulas": [],
"examples": [],
"related": [
"topic-template-derivative"
]
}
]
}
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