a) \(y' = - 2\left( {{x^2} - 4x + 3} \right)'.{\left( {{x^2} - 4x + 3} \right)^{ - 3}} \) \(= - 2\left( {2x - 4} \right){\left( {{x^2} - 4x + 3} \right)^{ - 3}} \) \(= - 4\left( {x - 2} \right){\left( {{x^2} - 4x + 3} \right)^{ - 3}}\)
b) \(y' = \dfrac{\pi }{3}{\left( {{x^3} - 8} \right)^{\frac{\pi }{3} - 1}}.\left( {{x^3} - 8} \right)' \) \(= \dfrac{\pi }{3}{\left( {{x^3} - 8} \right)^{\frac{\pi }{3} - 1}}.3{x^2} \) \(= \pi {x^2}{\left( {{x^3} - 8} \right)^{\frac{\pi }{3} - 1}}\)
c) \(y' = \dfrac{1}{4}{\left( {{x^3} - 3{x^2} + 2x} \right)^{\frac{1}{4} - 1}}\left( {{x^3} - 3{x^2} + 2x} \right)' \) \( = \dfrac{1}{4}{\left( {{x^3} - 3{x^2} + 2x} \right)^{ - \frac{3}{4}}}\left( {3{x^2} - 6x + 2} \right)\)
d) \(y' = - \dfrac{1}{3}{\left( {{x^2} + x - 6} \right)^{ - \frac{1}{3} - 1}}\left( {{x^2} + x - 6} \right)' \) \(= - \dfrac{1}{3}{\left( {{x^2} + x - 6} \right)^{ - \frac{4}{3}}}\left( {2x + 1} \right)\).
