Derivatives of Trigonometric Functions

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Previous Lecture

• Misc
  • Hour exam
    • Monday, Oct. 6
    • 4 - 6 short-answer questions, e.g., like problem sets
    • Whole class period
    • Open book, notes, computer; closed person
• Questions?
• Derivative of (6x² + 2x - 1)(x³ - 4x) / 7x²
  • (In Monday’s lecture notes)
• Derivatives of Trigonometric Functions
  • Section 3.5
    • d sinx / dx = cosx
    • d cosx / dx = -sinx
    • How do sin, cos, etc. examples work?
  • Examples: find f′(x) if...
    • f(x) = sinx - 3cosx
      • f′(x) = d sinx / dx - d (3cosx) / dx
      • = d sinx / dx - 3 d cosx / dx
      • = cosx + 3sinx
    • f(x) = (tanx)( x - sinx )
      • Product rule
        • d tanx / dx = sec²x
        • d (x-sinx) / dx = 1 - cosx
        • So f′(x) = tanx(1-cosx) + (x-sinx)sec²x
        • = tanx - tanx cosx + (x-sinx)sec²x
        • = tanx - sinx + (x-sinx)sec²x
        • = tanx - sinx + (x-sinx)(1/cos²x)
        • = tanx - sinx + (x-sinx)/cos²x
    • f(x) = (sinx) / (x + secx)
  • Problem set
• Next
  • The chain rule
  • Section 3.6

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