Basics of Differentiation Techniques Q1

Basics of Differentiation Techniques Q1

Tutorial

Differentiate the following expressions with respect to \(x\).

  1. \(\frac{4{{x}^{3}}+2{{x}^{2}}+1}{x}\)
  2. \(\mathrm{cose}{{\mathrm{c}}^{3}}\sqrt{x}\)
  3. \({{\cos }^{2}}\left( x{}^\circ \right)+\tan \left( x{}^\circ \right)\)
  4. \(\ln \sqrt{\frac{x-a}{x+a}}\) , where \(0 < a < x\)
  5. \(\lg \left( {{x}^{2}} \right)\) , where \(x<0\)
  6. \({{e}^{{{\sin }^{2}}x}}\left( {{e}^{-{{x}^{2}}}}+1 \right)\)

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Answer:See individual parts for derivatives

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