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Further Mathematics

Calculus

Key Points

  • d/dx(xⁿ) = nxⁿ⁻¹; d/dx(sin x) = cos x; d/dx(eˣ) = eˣ
  • Product rule: d/dx(uv) = u·v' + v·u'
  • Stationary points: set dy/dx = 0
  • ∫xⁿ dx = xⁿ⁺¹/(n+1) + C
  • Definite integral = area under curve between limits

Practice Questions

2 questions
1

Find dy/dx if y = 3x⁴ - 2x² + 5.

2

Evaluate ∫(2x + 3)dx

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Matrices & Vectors