READ_ONLY_ACCESS
[
  {
    "id": "maths1-w08-000",
    "front": "Definition of derivative $f'(x)$ from first principles",
    "back": "$\\lim_{h\\to 0} \\frac{f(x+h) - f(x)}{h}$"
  },
  {
    "id": "maths1-w08-001",
    "front": "Relationship between differentiability and continuity",
    "back": "Differentiable $\\implies$ Continuous (converse is FALSE)"
  },
  {
    "id": "maths1-w08-002",
    "front": "Power rule for differentiation $\\frac{d}{dx}[x^n]$",
    "back": "$n x^{n-1}$"
  },
  {
    "id": "maths1-w08-003",
    "front": "Product rule for differentiation $\\frac{d}{dx}[f(x)g(x)]$",
    "back": "$f'(x)g(x) + f(x)g'(x)$"
  },
  {
    "id": "maths1-w08-004",
    "front": "Quotient rule for differentiation $\\frac{d}{dx}\\left[\\frac{f(x)}{g(x)}\\right]$",
    "back": "$\\frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}$"
  },
  {
    "id": "maths1-w08-005",
    "front": "Chain rule for differentiation $\\frac{d}{dx}[f(g(x))]$",
    "back": "$f'(g(x)) \\cdot g'(x)$"
  },
  {
    "id": "maths1-w08-006",
    "front": "Critical point of $f(x)$ definition",
    "back": "Point in domain where $f'(x) = 0$ or $f'(x)$ is undefined"
  },
  {
    "id": "maths1-w08-007",
    "front": "L'Hôpital's rule condition",
    "back": "Applicable only to indeterminate forms $\\frac{0}{0}$ or $\\frac{\\pm\\infty}{\\pm\\infty}$"
  }
]