{
  "composicion-funciones": [
    {
      "title": "Composición de Funciones - Khan Academy",
      "url": "https://es.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:functions/x2ec2f6f830c9fb89:composing/v/function-composition",
      "type": "video",
      "description": "Introducción a la composición de funciones: notación f∘g y evaluación"
    },
    {
      "title": "Composing Functions - Math is Fun",
      "url": "https://www.mathsisfun.com/sets/functions-composition.html",
      "type": "article",
      "description": "Explicación visual de cómo evaluar f(g(x)) paso a paso"
    },
    {
      "title": "Identificar Funciones Internas y Externas",
      "url": "https://www.youtube.com/watch?v=identify-inner-outer",
      "type": "video",
      "description": "Técnicas para descomponer funciones compuestas correctamente"
    },
    {
      "title": "Function Composition Practice",
      "url": "https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:functions/x2ec2f6f830c9fb89:composing/e/compose-functions",
      "type": "practice",
      "description": "Ejercicios interactivos de composición de funciones"
    }
  ],
  "introduccion-cadena": [
    {
      "title": "Regla de la Cadena - Khan Academy",
      "url": "https://es.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1a/v/chain-rule-introduction",
      "type": "video",
      "description": "Introducción completa a la regla de la cadena con ejemplos básicos"
    },
    {
      "title": "Chain Rule - 3Blue1Brown",
      "url": "https://www.youtube.com/watch?v=YG15m2VwSjA",
      "type": "video",
      "description": "Visualización animada de por qué funciona la regla de la cadena"
    },
    {
      "title": "Chain Rule - Paul's Online Notes",
      "url": "https://tutorial.math.lamar.edu/classes/calci/chainrule.aspx",
      "type": "article",
      "description": "Explicación detallada con múltiples ejemplos resueltos"
    },
    {
      "title": "Regla de la Cadena en Español",
      "url": "https://www.youtube.com/watch?v=chain-rule-spanish",
      "type": "video",
      "description": "Tutorial completo en español con ejercicios paso a paso"
    },
    {
      "title": "Chain Rule Calculator",
      "url": "https://www.symbolab.com/solver/chain-rule-calculator",
      "type": "practice",
      "description": "Calculadora que muestra el proceso completo de la regla de la cadena"
    }
  ],
  "demostracion-cadena": [
    {
      "title": "Proof of Chain Rule - Khan Academy",
      "url": "https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1a/v/proof-of-chain-rule",
      "type": "video",
      "description": "Demostración formal de la regla de la cadena usando límites"
    },
    {
      "title": "Intuición Geométrica de la Cadena",
      "url": "https://www.youtube.com/watch?v=geometric-chain-intuition",
      "type": "video",
      "description": "Por qué dy/dx = dy/du · du/dx tiene sentido geométricamente"
    },
    {
      "title": "Chain Rule Intuition - Better Explained",
      "url": "https://betterexplained.com/articles/derivatives-product-power-chain/",
      "type": "article",
      "description": "Explicación intuitiva: tasas de cambio encadenadas"
    },
    {
      "title": "Notación de Leibniz para la Cadena",
      "url": "https://www.mathsisfun.com/calculus/derivatives-chain-rule.html",
      "type": "article",
      "description": "Por qué dy/dx = (dy/du)(du/dx) se ve como cancelación de fracciones"
    }
  ],
  "cadena-polinomios": [
    {
      "title": "Chain Rule with Polynomials",
      "url": "https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1a/e/chain-rule-polynomial",
      "type": "practice",
      "description": "Ejercicios: (2x+1)⁵, (x²-3)⁴, etc."
    },
    {
      "title": "Cadena con Funciones Polinomiales",
      "url": "https://www.youtube.com/watch?v=polynomial-chain-examples",
      "type": "video",
      "description": "Ejemplos variados de cadena con polinomios"
    },
    {
      "title": "Power Chain Rule Practice",
      "url": "https://www.symbolab.com/practice/chain-rule-practice",
      "type": "practice",
      "description": "Problemas de práctica con soluciones paso a paso"
    },
    {
      "title": "Ejercicios Resueltos - Polinomios",
      "url": "https://www.analyzemath.com/calculus/Differentiation/chain_rule_polynomial.html",
      "type": "article",
      "description": "Hoja de ejercicios con soluciones detalladas"
    }
  ],
  "cadena-trigonometricas": [
    {
      "title": "Chain Rule with Trig Functions",
      "url": "https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1b/v/chain-rule-trig",
      "type": "video",
      "description": "Cadena con sin(3x), cos(x²), tan(2x), etc."
    },
    {
      "title": "Derivadas Trigonométricas Compuestas",
      "url": "https://www.youtube.com/watch?v=trig-chain-rule",
      "type": "video",
      "description": "Técnicas especiales para funciones trigonométricas compuestas"
    },
    {
      "title": "Trig Chain Rule Examples",
      "url": "https://tutorial.math.lamar.edu/classes/calci/DiffTrigFcns.aspx",
      "type": "article",
      "description": "Ejemplos completos con trigonométricas"
    },
    {
      "title": "sin²(x) y cos²(x)",
      "url": "https://www.youtube.com/watch?v=trig-squared-derivatives",
      "type": "video",
      "description": "Cómo derivar potencias de funciones trigonométricas"
    },
    {
      "title": "Trig Chain Practice",
      "url": "https://www.symbolab.com/practice/trigonometric-chain-rule-practice",
      "type": "practice",
      "description": "Ejercicios interactivos con retroalimentación"
    }
  ],
  "cadena-exponenciales": [
    {
      "title": "Chain Rule with Exponentials",
      "url": "https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1c/v/chain-rule-exponential",
      "type": "video",
      "description": "Cadena con e^(2x), e^(x²), e^(sin(x)), etc."
    },
    {
      "title": "Derivadas de e^u y ln(u)",
      "url": "https://www.youtube.com/watch?v=exponential-logarithmic-chain",
      "type": "video",
      "description": "Regla de la cadena con funciones exponenciales y logarítmicas"
    },
    {
      "title": "Chain Rule: Exponential and Logarithmic",
      "url": "https://tutorial.math.lamar.edu/classes/calci/DiffExpLogFcns.aspx",
      "type": "article",
      "description": "Ejemplos detallados con e^u y ln(u)"
    },
    {
      "title": "Natural Log Chain Rule",
      "url": "https://www.youtube.com/watch?v=ln-chain-rule",
      "type": "video",
      "description": "Por qué d/dx[ln(f(x))] = f'(x)/f(x)"
    },
    {
      "title": "Exponential Chain Practice",
      "url": "https://www.symbolab.com/practice/exponential-chain-rule",
      "type": "practice",
      "description": "Problemas de práctica con e^u y ln(u)"
    }
  ],
  "cadenas-multiples": [
    {
      "title": "Multiple Chain Rule - Khan Academy",
      "url": "https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1d/v/multiple-chain-rule",
      "type": "video",
      "description": "Cadenas anidadas: sin(e^x), e^(sin(x)), [sin(2x)]³"
    },
    {
      "title": "Nested Functions - 3Blue1Brown",
      "url": "https://www.youtube.com/watch?v=nested-functions-calculus",
      "type": "video",
      "description": "Visualización de cómo derivar funciones profundamente anidadas"
    },
    {
      "title": "Cadenas Múltiples Paso a Paso",
      "url": "https://www.youtube.com/watch?v=multiple-chain-spanish",
      "type": "video",
      "description": "Tutorial en español: cómo trabajar con 3+ capas de composición"
    },
    {
      "title": "Complex Chain Rule Examples",
      "url": "https://tutorial.math.lamar.edu/classes/calci/chainrule.aspx#Complex",
      "type": "article",
      "description": "Ejemplos avanzados con composiciones múltiples"
    },
    {
      "title": "Nested Chain Calculator",
      "url": "https://www.derivative-calculator.net/",
      "type": "practice",
      "description": "Calculadora que muestra cada paso de cadenas múltiples"
    }
  ],
  "aplicaciones-cadena": [
    {
      "title": "Chain Rule Applications - Khan Academy",
      "url": "https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1e/v/chain-rule-applications",
      "type": "video",
      "description": "Aplicaciones en física, biología, economía"
    },
    {
      "title": "Related Rates with Chain Rule",
      "url": "https://www.youtube.com/watch?v=related-rates-chain",
      "type": "video",
      "description": "Problemas de tasas relacionadas usando la cadena"
    },
    {
      "title": "Crecimiento Exponencial y Cadena",
      "url": "https://www.youtube.com/watch?v=exponential-growth-chain",
      "type": "video",
      "description": "Modelos de población, decaimiento radiactivo, interés compuesto"
    },
    {
      "title": "Función Sigmoide (Machine Learning)",
      "url": "https://www.youtube.com/watch?v=sigmoid-derivative",
      "type": "video",
      "description": "Derivada de 1/(1+e^(-x)) - fundamental en redes neuronales"
    },
    {
      "title": "Chain Rule in Physics",
      "url": "https://www.youtube.com/watch?v=chain-rule-physics-applications",
      "type": "video",
      "description": "Velocidad, aceleración, movimiento armónico"
    },
    {
      "title": "Optimization with Chain Rule",
      "url": "https://tutorial.math.lamar.edu/classes/calci/Optimization.aspx",
      "type": "article",
      "description": "Problemas de optimización que requieren la cadena"
    },
    {
      "title": "Applied Chain Rule Problems",
      "url": "https://www.analyzemath.com/calculus/chain_rule/chain_rule_applications.html",
      "type": "practice",
      "description": "Problemas aplicados con soluciones completas"
    }
  ]
}