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Techniques of Differentiation - Product Rule

Techniques of Differentiation - Product Rule

Find the derivative of each of the following,

  1. \(y = (3x + 1)(x - 5)^{4}\)
  2. \(y = (4x - 3)(2x + 1)^{5}\)
  3. \(y = (1 - 2x)^{2}(3x + 1)^{3}\)
  4. \(y = (1 - 3x)^{2}(5x - 1)^{5}\)

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Answer:(a) \((x-5)^3(15x-11)\) (b) \(2(2x+1)^4(24x-13)\) (c) \(5(1-2x)(3x+1)^2(1-6x)\) (d) \((1-3x)(5x-1)^4(31-105x)\)

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