Đáp án:
b. \( - \dfrac{1}{{\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}\)
Giải thích các bước giải:
\(\begin{array}{l}
a.y = {x^4} - 4{x^2} - {x^2} + 4\\
= {x^4} - 5{x^2} + 4\\
y' = 4{x^3} - 10x\\
b.y = \left( {\sqrt x + 1} \right).\dfrac{1}{{\sqrt x - 1}}\\
= \dfrac{{\sqrt x + 1}}{{\sqrt x - 1}}\\
= \dfrac{{\dfrac{1}{{2\sqrt x }}\left( {\sqrt x - 1} \right) - \dfrac{1}{{2\sqrt x }}\left( {\sqrt x + 1} \right)}}{{{{\left( {\sqrt x - 1} \right)}^2}}}\\
= \dfrac{{\sqrt x - 1 - \sqrt x - 1}}{{2\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}\\
= \dfrac{{ - 2}}{{2\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}\\
= - \dfrac{1}{{\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}
\end{array}\)
