[
  {
    "term": "chain",
    "definition": "The chain rule differentiates a composition by multiplying the rate of the outer function with the rate of the inner function. Clear layer identification prevents missing factors."
  },
  {
    "term": "implicit",
    "definition": "Implicit differentiation treats y as a function of x even when the relation is not solved for y. Every derivative of a y-expression carries a dy/dx factor."
  },
  {
    "term": "inverse",
    "definition": "The derivative of an inverse reverses input and output while taking the reciprocal of the original slope at the corresponding point. A zero original slope prevents a finite inverse derivative."
  },
  {
    "term": "logdiff",
    "definition": "Logarithmic differentiation is useful when variables appear in both bases and exponents or when products and quotients contain many factors. Taking logarithms turns multiplicative structure into additive structure."
  }
]