\(\begin{array}{l}a)\,\,y = {\left( {{x^7} - 5{x^2}} \right)^3}\\ \Rightarrow y' = 3{\left( {{x^7} - 5{x^2}} \right)^2}\left( {{x^7} - 5{x^2}} \right)'\\\,\,\,\,\,\,y' = 3{\left( {{x^7} - 5{x^2}} \right)^2}.\left( {7{x^6} - 10x} \right)\\b)\,\,y = \left( {{x^2} + 1} \right)\left( {5 - 3{x^2}} \right)\\ \Rightarrow y = 5{x^2} - 3{x^4} + 5 - 3{x^2} = - 3{x^4} + 2{x^2} + 5\\ \Rightarrow y' = - 12{x^3} + 4x\\c)\,\,y = \dfrac{{2x}}{{{x^2} - 1}}\\ \Rightarrow y' = \dfrac{{2\left( {{x^2} - 1} \right) - 2x.2x}}{{{{\left( {{x^2} - 1} \right)}^2}}}\\\,\,\,\,\,\,y' = \dfrac{{2{x^2} - 2 - 4{x^2}}}{{{{\left( {{x^2} - 1} \right)}^2}}}\\\,\,\,\,\,\,y' = \dfrac{{ - 2{x^2} - 2}}{{{{\left( {{x^2} - 1} \right)}^2}}}\\d)\,\,y = \dfrac{{3 - 5x}}{{{x^2} - x + 1}}\\ \Rightarrow y' = \dfrac{{ - 5\left( {{x^2} - x + 1} \right) - \left( {3 - 5x} \right)\left( {2x - 1} \right)}}{{{{\left( {{x^2} - x + 1} \right)}^2}}}\\\,\,\,\,\,\,y' = \dfrac{{ - 5{x^2} + 5x - 5 + 3 - 11x + 10{x^2}}}{{{{\left( {{x^2} - x + 1} \right)}^2}}}\\\,\,\,\,\,\,y' = \dfrac{{5{x^2} - 6x - 2}}{{{{\left( {{x^2} - x + 1} \right)}^2}}}\\e)\,\,y = {\left( {m + \dfrac{n}{{{x^2}}}} \right)^3}\\ \Rightarrow y' = 3{\left( {m + \dfrac{n}{{{x^2}}}} \right)^2}\left( {m + \dfrac{n}{{{x^2}}}} \right)'\\\,\,\,\,\,\,y' = 3{\left( {m + \dfrac{n}{{{x^2}}}} \right)^2}.\left( {m + n.{x^{ - 2}}} \right)'\\\,\,\,\,\,\,y' = 3\left( {m + \dfrac{n}{{{x^2}}}} \right)^2.n.\left( { - 2} \right).{x^{ - 3}}\\\,\,\,\,\,y' = - 6n\left( {m + \dfrac{n}{{{x^2}}}} \right)^2.\dfrac{1}{{{x^3}}}\end{array}\)
