Bài tập 23 trang 205 SGK Toán 11 NC

a)

\(\begin{array}{l}
y\prime  = \frac{{2({x^2} - 5x + 5) - (2x + 3)(2x - 5)}}{{{{({x^2} - 5x + 5)}^2}}}\\
 = \frac{{ - 2{x^2} - 6x + 25}}{{{{({x^2} - 5x + 5)}^2}}}
\end{array}\)

b)

\(\begin{array}{l}
y\prime  = \frac{{ - 5({x^2} - x + 1)4(2x - 1)}}{{{{({x^2} - x + 1)}^{10}}}}\\
 = \frac{{ - 5(2x - 1)}}{{{{({x^2} - x + 1)}^6}}}
\end{array}\)

c) \(y\prime  = 2x + \sqrt x  + x.\frac{1}{{2\sqrt x }} = 2x + \frac{3}{2}\sqrt x \)

d)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
y\prime  = {(x + 2)^2}{(x + 3)^2}\\
 + (x + 1).2(x + 2){(x + 3)^3}\\
 + (x + 1){(x + 2)^2}3{(x + 3)^2}
\end{array}\\
{ = 2(x + 2){{(x + 3)}^2}(3{x^2} + 11x + 9)}
\end{array}\)

e) \(y\prime  = \frac{{1 - \frac{1}{{{x^2}}}}}{{2\sqrt {x + \frac{1}{x}} }} = \frac{{{x^2} - 1}}{{2{x^2}\sqrt {\frac{{{x^2} + 1}}{x}} }}\)

-- Mod Toán 11 HỌC247