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Techniques of Differentiation - Chain Rule

Techniques of Differentiation - Chain Rule

TGM Original Questions

Differentiate each of the following with respect to \(x\).

  1. \(y = (2x^2 - 3x + 4)^{\frac{5}{2}}\)
  2. \(y = (2x^3 - x + 1)^{14}\)
  3. \(y = \sqrt{(4x^2 + 3x + 5)^9}\)
  4. \(y = (2\sqrt{x} + 4x)^2\)

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Answer:(i) \(\dfrac52(2x^2-3x+4)^{3/2}(4x-3)\) (ii) \(14(2x^3-x+1)^{13}(6x^2-1)\) (iii) \(\dfrac92(4x^2+3x+5)^{7/2}(8x+3)\) (iv) \(2(2\sqrt{x}+4x)\left(\dfrac1{\sqrt{x}}+4\right)\)

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