DIFFERENTIATION RULES:
  Power: d/dx(xⁿ) = nxⁿ⁻¹
  Product: d/dx(uv) = u'v + uv'
  Quotient: d/dx(u/v) = (u'v - uv')/v²
  Chain: d/dx[f(g(x))] = f'(g(x)) × g'(x)
  Implicit: differentiate both sides with respect to x
  
  IMPORTANT DERIVATIVES:
    d/dx(sin x) = cos x | d/dx(cos x) = -sin x
    d/dx(tan x) = sec²x | d/dx(ln x) = 1/x
    d/dx(eˣ) = eˣ | d/dx(aˣ) = aˣ ln a

INTEGRATION TECHNIQUES:
  Substitution: let u = g(x), du = g'(x)dx
  By Parts: ∫u dv = uv - ∫v du (ILATE: Inverse/Log/Algebraic/Trig/Exponential)
  Partial Fractions: decompose rational function into simpler fractions
  
  STANDARD INTEGRALS (must memorise):
    ∫xⁿdx = xⁿ⁺¹/(n+1) | ∫1/x dx = ln|x| | ∫eˣdx = eˣ
    ∫sin x dx = -cos x | ∫cos x dx = sin x | ∫sec²x dx = tan x
    ∫1/(a²+x²)dx = (1/a)tan⁻¹(x/a) | ∫1/√(a²-x²)dx = sin⁻¹(x/a)

  DEFINITE INTEGRAL PROPERTIES:
    ∫[a to b] f(x)dx = -∫[b to a] f(x)dx
    ∫[0 to 2a] f(x)dx = 2∫[0 to a] f(x)dx if f(2a-x) = f(x)
    ∫[-a to a] f(x)dx = 2∫[0 to a] f(x)dx if f(-x) = f(x) (even function)
    ∫[-a to a] f(x)dx = 0 if f(-x) = -f(x) (odd function)

APPLICATIONS OF DERIVATIVES:
  Tangent at (x₁,y₁): y-y₁ = m(x-x₁) where m = dy/dx at that point
  Normal: slope = -1/m (perpendicular to tangent)
  Increasing: dy/dx > 0 | Decreasing: dy/dx < 0
  Maxima: dy/dx = 0 and d²y/dx² < 0 | Minima: d²y/dx² > 0

CIRCLES:
  General equation: x²+y²+2gx+2fy+c = 0
  Centre: (-g,-f) | Radius: √(g²+f²-c)
  Tangent at (x₁,y₁): xx₁+yy₁+g(x+x₁)+f(y+y₁)+c = 0
  
  Length of tangent from external point (x₁,y₁): √(x₁²+y₁²+2gx₁+2fy₁+c)

PARABOLA (y² = 4ax, a>0):
  Focus: (a,0) | Directrix: x = -a | Vertex: (0,0)
  Point on parabola: (at², 2at)
  Tangent at t: ty = x + at²
  Normal at t: y + tx = 2at + at³

ELLIPSE (x²/a² + y²/b² = 1, a>b):
  Eccentricity: e = c/a where c² = a²-b²
  Foci: (±c, 0) | Directrices: x = ±a/e
  Sum of focal distances from any point = 2a (constant)