ĐGNL ĐHQG Hà Nội - Tư duy định lượng - Đạo hàm cấp cao

A.\[dy = {\left( {{x^2} + 2x} \right)^\prime }dx\]

B. \[dx = {\left( {{x^2} + 2x} \right)^\prime }dy\]

C. \[dy = \left( {{x^2} + 2x} \right)dx\]

D. \[dy = \frac{1}{{{x^2} + 2x}}dx\]

A.\[y'' = 0\]

B. \[y'' = \frac{1}{{{{\left( {x - 2} \right)}^2}}}\]

C. \[y'' = - \frac{4}{{{{\left( {x - 2} \right)}^3}}}\]

D. \[y'' = \frac{4}{{{{\left( {x - 2} \right)}^3}}}\]

A.\[y''' = 12x\left( {{x^2} + 1} \right)\]

B. \[y''' = 24x\left( {{x^2} + 1} \right)\]

C. \[y''' = 24x\left( {5{x^2} + 3} \right)\]

D. \[y''' = - 12x\left( {{x^2} + 1} \right)\]

A.\[y'' = \frac{1}{{\left( {2x + 5} \right)\sqrt {2x + 5} }}\]

B.\[y'' = \frac{1}{{\sqrt {2x + 5} }}\]

C. \[y'' = - \frac{1}{{\left( {2x + 5} \right)\sqrt {2x + 5} }}\]

D. \[y'' = - \frac{1}{{\sqrt {2x + 5} }}\]

A.\[y'' = - \frac{{2\sin x}}{{{{\cos }^3}x}}\]

B. \[y'' = \frac{1}{{{{\cos }^2}x}}\]

C. \[y'' = - \frac{1}{{{{\cos }^2}x}}\]

D. \[y'' = \frac{{2\sin x}}{{{{\cos }^3}x}}\]

A.M=0.

B.M=20.

C.M=40.

D.M=100.

A.\[\left[ { - 1;2} \right]\]

B. \[\left( { - \infty ;0} \right]\]

C. \[\left\{ { - 1} \right\}\]

D. \[\emptyset \]

A.\[y' = \sin \left( {x + \frac{\pi }{2}} \right)\]

B. \[y'' = \sin \left( {x + \pi } \right)\]

C. \[y''' = \sin \left( {x + \frac{{3\pi }}{2}} \right)\]

D. \[{y^{\left( 4 \right)}} = \sin \left( {2\pi - x} \right)\]

A.\[x = \frac{\pi }{2}\]

B. \[x = 0\]hoặc \[x = \frac{\pi }{6}\]

C. \[x = 0\]hoặc\[x = \frac{\pi }{3}\]

D. \[x = 0\]hoặc \[x = \frac{\pi }{2}\]

A.\[4y - y'' = 0\]

B. \[4y + y'' = 0\]

C. \[y = y'\tan 2x\]

D. \[{y^2} = {\left( {y'} \right)^2} = 4\]

A.Chỉ (I)

B.Chỉ (II) đúng

C.Cả hai đều đúng

D.Cả hai đều sai

A.0

B.1

C.−2

D.5

A.\[x \in \left( {1; + \infty } \right).\]

B. \[x \in \left( { - \infty ;1} \right) \setminus \left\{ 0 \right\}.\]

C. \[x \in \left( { - 1;1} \right).\]

D. \[x \in \left( { - 2;2} \right).\]

A.\[\frac{1}{{\cos x}}\]

B. \[ - \frac{1}{{\cos x}}\]

C. \[\cot x\]

D. \[\tan x\]

A.\[{f^{\left( {10} \right)}}\left( 1 \right) = 0\]

B. \[{f^{\left( {10} \right)}}\left( 1 \right) = 10a + b\]

C. \[{f^{\left( {10} \right)}}\left( 1 \right) = 5a\]

D. \[{f^{\left( {10} \right)}}\left( 1 \right) = 10a\]

A.−cosx 

B.sinx 

C.−sinx 

D.cosx 

A.\[12\,m/{s^2}\]

B. \[8\,m/{s^2}\]

C. \[7\,m/{s^2}\]

D. \[6\,m/{s^2}\]

A.\[{y^{\left( 4 \right)}} = - 2048\cos 8x + 8\cos 2x\]

B. \[{y^{\left( 4 \right)}} = 2048\cos 8x - 8\cos 2x\]

C. \[{y^{\left( 4 \right)}} = 1024\cos 16x + 4\cos 4x\]

D. \[{y^{\left( 4 \right)}} = 2048\cos 8x - 4\cos 4x\]

A.\[{y^3}.y'' + 1 = 0\]

B. \[{y^2}.y'' - 1 = 0\]

C. \[3{y^2}.y'' + 1 = 0\]

D. \[2{y^3}.y'' + 3 = 0\]

A.\[{y^{\left( n \right)}} = \frac{{{2^n}.{a^n}.n!}}{{{{\left( {ax + b} \right)}^{n + 1}}}}\]

B. \[{y^{\left( n \right)}} = \frac{{{{\left( { - 1} \right)}^n}{a^n}n!}}{{{{\left( {x + 1} \right)}^{n + 1}}}}\]

C. \[{y^{\left( n \right)}} = \frac{{{{\left( { - 1} \right)}^n}.n!}}{{{{\left( {ax + b} \right)}^{n + 1}}}}\]

D. \[{y^{\left( n \right)}} = \frac{{{{\left( { - 1} \right)}^n}.{a^n}.n!}}{{{{\left( {ax + b} \right)}^{n + 1}}}}\]

A.\[{y^{\left( 4 \right)}} = \frac{{7.4!}}{{{{\left( {x - 3} \right)}^5}}} - \frac{{5.4!}}{{{{\left( {x - 2} \right)}^5}}}\]

B. \[{y^{\left( 4 \right)}} = \frac{{5.4!}}{{{{\left( {x - 3} \right)}^5}}} - \frac{{2.4!}}{{{{\left( {x - 2} \right)}^5}}}\]

C. \[{y^{\left( 4 \right)}} = \frac{{5.4!}}{{{{\left( {x - 2} \right)}^5}}} - \frac{{7.4!}}{{{{\left( {x - 3} \right)}^5}}}\]

D. \[{y^{\left( 4 \right)}} = \frac{7}{{{{\left( {x - 3} \right)}^4}}} - \frac{5}{{{{\left( {x - 2} \right)}^4}}}\]

A.6

B.2020

C.2021

D.0