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"collections": [
{
"id": "long_walkthroughs",
"name": "Long Walkthrough Demos",
"description": "Each demo produces at least 5 animation steps for testing.",
"demos": [
{
"id": "fifth_product_chain",
"title": "5th Derivative: Product + Chain",
"subtitle": "d^5/dx^5 of x^3 sin(x^2)",
"latex": "\\frac{d^5}{dx^5} (x^3 \\sin(x^2))",
"tag": "derivative",
"params": {"variable": "x", "order": 5},
"notes": [
"Generates 6+ steps",
"Includes product-rule structure",
"Shows repeated differentiation progression"
]
},
{
"id": "sixth_exp_product",
"title": "6th Derivative: Polynomial * Exponential",
"subtitle": "d^6/dx^6 of x^2 e^x",
"latex": "\\frac{d^6}{dx^6} (x^2 e^{x})",
"tag": "derivative",
"params": {"variable": "x", "order": 6},
"notes": [
"Generates 8+ steps",
"Great for long animation playback",
"Clear left-to-right step chaining"
]
},
{
"id": "fifth_quotient",
"title": "5th Derivative: Quotient + Trig",
"subtitle": "d^5/dx^5 of (x^2 + 1)/cos(x)",
"latex": "\\frac{d^5}{dx^5} \\frac{x^2 + 1}{\\cos(x)}",
"tag": "derivative",
"params": {"variable": "x", "order": 5},
"notes": [
"Generates 7+ steps",
"Uses quotient-rule behavior",
"Good stress test for symbol motion"
]
},
{
"id": "fifth_log",
"title": "5th Derivative: Log Composite",
"subtitle": "d^5/dx^5 of ln(x^2 + 1)",
"latex": "\\frac{d^5}{dx^5} \\ln(x^2+1)",
"tag": "derivative",
"params": {"variable": "x", "order": 5},
"notes": [
"Generates 7+ steps",
"Chain behavior appears repeatedly",
"Good for readability checks"
]
},
{
"id": "fifth_trig_product",
"title": "5th Derivative: Trig Product",
"subtitle": "d^5/dx^5 of sin(x)cos(x)",
"latex": "\\frac{d^5}{dx^5} (\\sin(x)\\cos(x))",
"tag": "derivative",
"params": {"variable": "x", "order": 5},
"notes": [
"Generates 9+ steps",
"Alternating trig forms are easy to track",
"Ideal for testing long deterministic animations"
]
}
]
}
]
}
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