Bài tập 19 trang 204 SGK Toán 11 NC

a) \(y\prime  = 32{(x - x2)^{31}}(1 - 2x)\)

b)

\(\begin{array}{l}
y\prime  =  - \frac{{(x\sqrt x )\prime }}{{{x^3}}} =  - \frac{{\sqrt x  + \frac{x}{{2\sqrt x }}}}{{{x^3}}}\\
 = \frac{{ - 3x}}{{2\sqrt x .{x^3}}} = \frac{{ - 3}}{{2{x^2}\sqrt x }}
\end{array}\)

c)

\(\begin{array}{l}
y\prime  = \frac{{\sqrt {1 - x}  - (1 + x).\frac{{ - 1}}{{2\sqrt {1 - x} }}}}{{1 - x}}\\
 = \frac{{2(1 - x) + 1 + x}}{{2\sqrt {{{(1 - x)}^3}} }} = \frac{{3 - x}}{{2\sqrt {{{(1 - x)}^3}} }}
\end{array}\)

d)

\(\begin{array}{l}
y\prime  = \frac{{\sqrt {{a^2} - {x^2}}  - x.\frac{{ - 2x}}{{2\sqrt {{a^2} - {x^2}} }}}}{{{{(\sqrt {{a^2} - {x^2}} )}^2}}}\\
 = \frac{{2\left( {{a^2} - {x^2}} \right) + 2{x^2}}}{{2{{\left( {\sqrt {{a^2} - {x^2}} } \right)}^3}}} = \frac{{{a^2}}}{{\sqrt {{{\left( {{a^2} - {x^2}} \right)}^3}} }}
\end{array}\)

-- Mod Toán 11 HỌC247