Tính đạo hàm

a) \(y = \sqrt {2{x^2} - 5x + 2} \);

b) \(y = \tan 2x - \frac{1}{3}\cot 4x + \sqrt {\sin x} \);

c) \(y = \frac{{{{\left( {2x + 1} \right)}^2}}}{{{{\left( {x - 1} \right)}^3}}}\).

a) \(y' = \frac{{{{\left( {2{x^2} - 5x + 2} \right)}^\prime }}}{{2\sqrt {2{x^2} - 5x + 2} }} = \frac{{4x - 5}}{{2\sqrt {2{x^2} - 5x + 2} }}\).

b) \(y' = {\left( {\tan 2x} \right)^\prime } - \frac{1}{3}{\left( {\cot 4x} \right)^\prime } + {\left( {\sqrt {\sin x} } \right)^\prime } = \frac{2}{{{{\cos }^2}2x}} + \frac{4}{{3{{\sin }^2}4x}} + \frac{{\cos x}}{{2\sqrt {\sin x} }}\).

c)  \(y' = \frac{{{{\left[ {{{\left( {2x + 1} \right)}^2}} \right]}^\prime }{{\left( {x - 1} \right)}^3} - {{\left( {2x + 1} \right)}^2}{{\left[ {{{\left( {x - 1} \right)}^3}} \right]}^\prime }}}{{{{\left( {x - 1} \right)}^6}}}\)

\(\begin{array}{l} = \frac{{4\left( {2x + 1} \right){{\left( {x - 1} \right)}^3} - {{\left( {2x + 1} \right)}^2}3{{\left( {x - 1} \right)}^2}}}{{{{\left( {x - 1} \right)}^6}}} = \frac{{4\left( {2x + 1} \right)\left( {x - 1} \right) - {{\left( {2x + 1} \right)}^2}3}}{{{{\left( {x - 1} \right)}^4}}}\\ = \frac{{ - 4{x^2} - 16x - 7}}{{{{\left( {x - 1} \right)}^4}}}.\end{array}\)