Differentiation - Power Rule and Derivatives of Algebraic Functions

Differentiation - Power Rule and Derivatives of Algebraic Functions

Find the derivative of each of the following,

  1. \(\mathrm{f}(x) = -5x^8 + 4\sqrt[3]{x}\)
  2. \(\mathrm{f}(x) = \sqrt[3]{x} - 2x^5 + 3\)
  3. \(y = 7x^3 + \frac{2}{\sqrt{x}} + \frac{3}{x^5}\)

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Answer:(a) \(-40x^7+\frac{4}{3}x^{-\frac{2}{3}}\) (b) \(\frac{1}{3}x^{-\frac{2}{3}}-10x^4\) (c) \(21x^2-x^{-\frac{3}{2}}-15x^{-6}\)

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