Bài tập 18 trang 204 SGK Toán 11 NC

Bài tập 18 trang 204 SGK Toán 11 NC

a)

\(\begin{array}{l}
y = {\left( {{x^7} + x} \right)^2} = {x^{14}} + 2{x^8} + {x^2}\\
 \Rightarrow y\prime  = 14{x^{13}} + 16{x^7} + 2x
\end{array}\)

b)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
y\prime  = ({x^2} + 1)\prime (5 - 3{x^2})\\
 + ({x^2} + 1)(5 - 3{x^2})\prime 
\end{array}\\
\begin{array}{l}
 = 2x(5 - 3{x^2}) - 6x({x^2} + 1)\\
 = 4x - 12{x^3}
\end{array}
\end{array}\)

c)

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

d)

\(\begin{array}{l}
y\prime  = \frac{{5({x^2} + x + 1) - (5x - 3)(2x + 1)}}{{{{({x^2} + x + 1)}^2}}}\\
 = \frac{{ - 5{x^2} + 6x + 8}}{{{{(x2 + x + 1)}^2}}}
\end{array}\)

e)

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

f)

\(\begin{array}{l}
y = (2{x^2} - x)(3x + 2)\\
 \Rightarrow y\prime  = (4x - 1)(3x + 2) + {(2{x^2} - x)^3}\\
 = 18{x^2} + 2x - 2
\end{array}\)

-- Mod Toán 11