Bài tập 18 trang 73 SBT Toán 11 Tập 2 Cánh diều - CD

a) Ta có: \({f'}\left( x \right) = {\left( {2\cos \left( {\sqrt x } \right)} \right)^\prime }\)

\(= 2{\left( {\sqrt x } \right)^\prime }.\left( { - \sin \left( {\sqrt x } \right)} \right) = \frac{2}{{2\sqrt x }}.\left( { - \sin \left( {\sqrt x } \right)} \right) \\= \frac{{ - \sin \left( {\sqrt x } \right)}}{{\sqrt x }}.\)

b) Ta có: \(g'\left( x \right) = {\left( {\tan \left( {{x^2}} \right)} \right)^\prime }\)

\(= \frac{{{{\left( {{x^2}} \right)}^\prime }}}{{{{\cos }^2}\left( {{x^2}} \right)}} \\= \frac{{2x}}{{{{\cos }^2}\left( {{x^2}} \right)}}.\)

c) Ta có: \(h\left( x \right) = {\rm{co}}{{\rm{s}}^2}\left( {3x} \right) - {\rm{si}}{{\rm{n}}^2}\left( {3x} \right) = \cos \left( {6x} \right).\)

\( \Rightarrow h'\left( x \right) = {\left( {\cos \left( {6x} \right)} \right)^\prime } = {\left( {6x} \right)^\prime }.\left( { - \sin \left( {6x} \right)} \right) = - 6\sin \left( {6x} \right).\)

d) Ta có: \(k'\left( x \right) = {\left( {{{\sin }^2}\left( x \right)} \right)^\prime } + {\left( {{e^x}.\sqrt x } \right)^\prime } \)

\(= 2\sin x{\left( {\sin x} \right)^\prime } + {\left( {{e^x}} \right)^\prime }.\sqrt x + {\left( {\sqrt x } \right)^\prime }.{e^x}\)

\( = 2\sin x\cos x + {e^x}.\sqrt x + \frac{{{e^x}}}{{2\sqrt x }}.\)

-- Mod Toán 11 HỌC247