[
  {
    "term": "exp derivative",
    "definition": "Exponential derivatives preserve exponential structure. The natural exponential function is its own derivative; other bases introduce a logarithmic scale factor."
  },
  {
    "term": "log derivative",
    "definition": "Logarithmic derivatives convert multiplicative structure into reciprocal rates. Domain restrictions remain essential because real logarithms require positive arguments."
  },
  {
    "term": "motion",
    "definition": "Position, velocity, and acceleration are successive layers of change. Their signs and zeros describe direction, speed changes, turning, and concavity, while their units distinguish the quantities."
  },
  {
    "term": "rules",
    "definition": "Differentiation rules compress repeated limit arguments into reliable structures. Each rule should be chosen from the algebraic form of the function and verified through units, graph behavior, or a numerical derivative."
  },
  {
    "term": "trig derivative",
    "definition": "Trigonometric derivatives connect periodic position with periodic rates. Angle measure must be in radians for the standard derivative formulas to hold without an additional conversion factor."
  }
]