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Techniques of Differentiation - Quotient Rule

Techniques of Differentiation - Quotient Rule

TGM Original Questions

Find the derivative of each of the following functions with respect to \(x\).

  1. \(f(x) = \frac{2x^3}{3x - 2}\)
  2. \(f(x) = \frac{x}{\sqrt{x^2 + 3x + 2}}\)
  3. \(f(x) = \frac{3(1 - x - x^2)}{(x^2 + 1)^2}\)
  4. \(f(x) = \frac{x}{\sqrt{3 - 2x}}\)

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Answer:(i) \(\dfrac{12x^2(x-1)}{(3x-2)^2}\) (ii) \(\dfrac{3x+4}{2(x^2+3x+2)^{3/2}}\) (iii) \(\dfrac{3(2x^3+3x^2-6x-1)}{(x^2+1)^3}\) (iv) \(\dfrac{3-x}{(3-2x)^{3/2}}\)

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