data/formulas.json

{
  "categories": [
    {"id": "derivatives", "name": "Derivatives", "icon": "∂"},
    {"id": "integrals", "name": "Integrals", "icon": "∫"},
    {"id": "limits", "name": "Limits", "icon": "lim"},
    {"id": "series", "name": "Series", "icon": "Σ"}
  ],
  "formulas": [
    {
      "id": "power_rule",
      "category": "derivatives",
      "name": "Power Rule",
      "latex": "\\frac{d}{dx} x^3",
      "tag": "derivative",
      "params": {"variable": "x"},
      "description": "Derivative of x³"
    },
    {
      "id": "product_rule_ex",
      "category": "derivatives",
      "name": "Product Rule",
      "latex": "\\frac{d}{dx} x \\sin(x)",
      "tag": "derivative",
      "params": {"variable": "x"},
      "description": "Product rule example"
    },
    {
      "id": "chain_rule_ex",
      "category": "derivatives",
      "name": "Chain Rule",
      "latex": "\\frac{d}{dx} \\sin(x^2)",
      "tag": "derivative",
      "params": {"variable": "x"},
      "description": "Chain rule example"
    },
    {
      "id": "quotient_ex",
      "category": "derivatives",
      "name": "Quotient Rule",
      "latex": "\\frac{d}{dx} \\frac{x}{\\cos(x)}",
      "tag": "derivative",
      "params": {"variable": "x"},
      "description": "Quotient rule example"
    },
    {
      "id": "exp_deriv",
      "category": "derivatives",
      "name": "Exponential",
      "latex": "\\frac{d}{dx} e^{2x}",
      "tag": "derivative",
      "params": {"variable": "x"},
      "description": "Derivative of e^(2x)"
    },
    {
      "id": "log_deriv",
      "category": "derivatives",
      "name": "Logarithmic",
      "latex": "\\frac{d}{dx} \\ln(x^2 + 1)",
      "tag": "derivative",
      "params": {"variable": "x"},
      "description": "Derivative of ln(x²+1)"
    },
    {
      "id": "second_deriv",
      "category": "derivatives",
      "name": "Second Derivative",
      "latex": "\\frac{d^2}{dx^2} x^4",
      "tag": "derivative",
      "params": {"variable": "x", "order": 2},
      "description": "Second derivative of x⁴"
    },
    {
      "id": "poly_integral",
      "category": "integrals",
      "name": "Polynomial",
      "latex": "\\int x^3 + 2x \\, dx",
      "tag": "integral",
      "params": {"variable": "x"},
      "description": "Integral of x³ + 2x"
    },
    {
      "id": "trig_integral",
      "category": "integrals",
      "name": "Trig Integral",
      "latex": "\\int \\sin(x) \\, dx",
      "tag": "integral",
      "params": {"variable": "x"},
      "description": "Integral of sin(x)"
    },
    {
      "id": "exp_integral",
      "category": "integrals",
      "name": "Exponential",
      "latex": "\\int e^{-x} \\, dx",
      "tag": "integral",
      "params": {"variable": "x"},
      "description": "Integral of e^(-x)"
    },
    {
      "id": "def_integral_x2",
      "category": "integrals",
      "name": "Definite ∫ x²",
      "latex": "\\int_0^1 x^2 \\, dx",
      "tag": "definite_integral",
      "params": {"variable": "x", "lower": 0, "upper": 1},
      "description": "∫₀¹ x² dx"
    },
    {
      "id": "def_integral_sin",
      "category": "integrals",
      "name": "Definite ∫ sin",
      "latex": "\\int_0^{\\pi} \\sin(x) \\, dx",
      "tag": "definite_integral",
      "params": {"variable": "x", "lower": 0, "upper": 3.14159},
      "description": "∫₀^π sin(x) dx"
    },
    {
      "id": "sinc_limit",
      "category": "limits",
      "name": "sin(x)/x",
      "latex": "\\lim_{x \\to 0} \\frac{\\sin(x)}{x}",
      "tag": "limit",
      "params": {"variable": "x", "point": "0"},
      "description": "Classic sinc limit"
    },
    {
      "id": "inf_limit",
      "category": "limits",
      "name": "Limit at ∞",
      "latex": "\\lim_{x \\to \\infty} \\frac{1}{x}",
      "tag": "limit",
      "params": {"variable": "x", "point": "oo"},
      "description": "Limit as x → ∞"
    },
    {
      "id": "exp_limit",
      "category": "limits",
      "name": "e definition",
      "latex": "\\lim_{x \\to \\infty} (1 + \\frac{1}{x})^x",
      "tag": "limit",
      "params": {"variable": "x", "point": "oo"},
      "description": "Limit definition of e"
    },
    {
      "id": "lhopital_ex",
      "category": "limits",
      "name": "L'Hôpital",
      "latex": "\\lim_{x \\to 0} \\frac{e^x - 1}{x}",
      "tag": "limit",
      "params": {"variable": "x", "point": "0"},
      "description": "L'Hôpital's rule example"
    },
    {
      "id": "taylor_sin",
      "category": "series",
      "name": "Taylor sin(x)",
      "latex": "\\sin(x)",
      "tag": "taylor",
      "params": {"variable": "x", "point": 0, "order": 7},
      "description": "Taylor series of sin(x)"
    },
    {
      "id": "taylor_exp",
      "category": "series",
      "name": "Taylor eˣ",
      "latex": "e^x",
      "tag": "taylor",
      "params": {"variable": "x", "point": 0, "order": 6},
      "description": "Taylor series of eˣ"
    },
    {
      "id": "taylor_cos",
      "category": "series",
      "name": "Taylor cos(x)",
      "latex": "\\cos(x)",
      "tag": "taylor",
      "params": {"variable": "x", "point": 0, "order": 6},
      "description": "Taylor series of cos(x)"
    },
    {
      "id": "taylor_ln",
      "category": "series",
      "name": "Taylor ln(1+x)",
      "latex": "\\ln(1+x)",
      "tag": "taylor",
      "params": {"variable": "x", "point": 0, "order": 6},
      "description": "Taylor series of ln(1+x)"
    }
  ]
}