Bài tập 21 trang 226 SGK Toán 11 NC

Bài tập 21 trang 226 SGK Toán 11 NC

a.

\(\begin{array}{l}
y' = \left[ {\frac{a}{{a + b}}{x^2} + \frac{b}{{a + b}}x + \frac{c}{{\left( {a + b} \right)x}}} \right]\\
 = \frac{{2a}}{{a + b}}x + \frac{b}{{a + b}} - \frac{c}{{\left( {a + b} \right){x^2}}}\\
 = \frac{{2a{x^3} + b{x^2} - c}}{{\left( {a + b} \right){x^2}}}
\end{array}\)

b.

\(\begin{array}{l}
y' = 4{\left( {{x^3} - \frac{1}{{{x^3}}} + 3} \right)^3}\left( {3{x^2} + \frac{3}{{{x^4}}}} \right)\\
 = 12\left( {{x^3} - \frac{1}{{{x^3}}} + 3} \right)\left( {{x^2} + \frac{1}{{{x^4}}}} \right)
\end{array}\)

c. 

\(\begin{array}{l}
y' = 3{x^2}{\cos ^2}x - {x^3}\sin 2x\\
 = {x^2}\left( {3{{\cos }^2}x - x\sin 2x} \right)
\end{array}\)

d. 

\(y' = \frac{x}{{\sqrt {4 + {x^2}} }}\cos \sqrt {4 + {x^2}} \)

e.

\(\begin{array}{l}
y' = \frac{{1 - \frac{1}{{{x^2}}}}}{{2{{\cos }^2}\left( {x + \frac{1}{x}} \right)\sqrt {1 + \tan \left( {x + \frac{1}{x}} \right)} }}\\
 = \frac{{{x^2} - 1}}{{2{x^2}{{\cos }^2}\left( {x + \frac{1}{x}} \right)\sqrt {1 + \tan \left( {x + \frac{1}{x}} \right)} }}
\end{array}\)

-- Mod Toán 11