\(\begin{array}{l}a)\,\,y = {x^2} - x\sqrt x + 1\\ \Rightarrow y' = 2x - \left( {\sqrt x + x.\dfrac{1}{{2\sqrt x }}} \right)\\\,\,\,\,\,\,y' = 2x - \sqrt x - \dfrac{{\sqrt x }}{2}\\\,\,\,\,\,\,y' = 2x - \dfrac{{3\sqrt x }}{2}\\b)\,\,y = \sqrt {2 - 5x - {x^2}} \\ \Rightarrow y' = \dfrac{{\left( {2 - 5x - {x^2}} \right)'}}{{2\sqrt {2 - 5x - {x^2}} }}\\\,\,\,\,\,y' = \dfrac{{ - 2x - 5}}{{2\sqrt {2 - 5x - {x^2}} }}\\c)\,\,y = \dfrac{{{x^3}}}{{\sqrt {{a^2} - {x^2}} }}\,\,\left( {a = const} \right)\\ \Rightarrow y' = \dfrac{{3{x^2}\sqrt {{a^2} - {x^2}} - {x^3}.\dfrac{{ - 2x}}{{2\sqrt {{a^2} - {x^2}} }}}}{{{a^2} - {x^2}}}\\\,\,\,\,\,\,y' = \dfrac{{3{x^2}\left( {{a^2} - {x^2}} \right) + {x^4}}}{{{{\left( {\sqrt {{a^2} - {x^2}} } \right)}^3}}}\\\,\,\,\,\,\,y' = \dfrac{{3{x^2}{a^2} - 2{x^4}}}{{{{\left( {\sqrt {{a^2} - {x^2}} } \right)}^3}}}\\d)\,\,y = \dfrac{{1 + x}}{{\sqrt {1 - x} }}\\ \Rightarrow y' = \dfrac{{\sqrt {1 - x} - \left( {1 + x} \right)\dfrac{{ - 1}}{{2\sqrt {1 - x} }}}}{{1 - x}}\\\,\,\,\,\,\,y' = \dfrac{{2\left( {1 - x} \right) + \left( {1 + x} \right)}}{{2{{\left( {\sqrt {1 - x} } \right)}^3}}}\\\,\,\,\,\,\,y' = \dfrac{{3 - x}}{{2{{\left( {\sqrt {1 - x} } \right)}^3}}}\end{array}\)
