data/demo_problems.json

{
  "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"
          ]
        }
      ]
    }
  ]
}