{
  "schema": "ml-prep/item@1",
  "item": {
    "id": "mit-18-02sc-f2010-exam2-q4",
    "area": "mathematics",
    "topic": "calculus",
    "origin": "external",
    "title": "Multivariable chain rule under a change of variables",
    "skills": [
      "chain-rule",
      "partial-derivatives"
    ],
    "priority": "core",
    "difficulty": "medium",
    "estimated_minutes": 10,
    "prerequisites": [
      "partial-derivatives"
    ],
    "source_id": "mit-18-02sc-f2010",
    "locator": {
      "document": "Exam 2",
      "label": "Question 4(a–c)",
      "page": 1,
      "solution_pages": "1"
    },
    "links": {
      "problem": "https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/resources/mit18_02sc_exam2/",
      "solution": "https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/resources/mit18_02sc_exam2sol/"
    },
    "selection_note": "Tests symbolic chain-rule bookkeeping that directly supports backpropagation and reparameterization.",
    "answer_status": "official-solution"
  }
}