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

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Answer:(i) \(\dfrac{3x^2-2x-3}{(3x-1)^2}\) (ii) \(-\dfrac{4x+1}{(2x^2-1)^{3/2}}\) (iii) \(\dfrac{8x^4-50x^3+12x^2+4x-10}{(x^2-5x+1)^{3/2}}\) (iv) \(\dfrac{23-4x}{(5-2x)^{3/2}}\)

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