ĐGNL ĐHQG Hà Nội - Tư duy định lượng - Các quy tắc tính đạo hàm

A.\[y' = 4{x^3} - 6x + 3\]

B. \[y' = 4{x^4} - 6x + 2\]

C. \[y' = 4{x^3} - 3x + 2\]

D. \[y' = 4{x^3} - 6x + 2\]

A.\[ - \frac{3}{{{{\left( {x + 2} \right)}^2}}}\]

B. \[\frac{3}{{x + 2}}\]

C. \[\frac{3}{{{{\left( {x + 2} \right)}^2}}}\]

D. \[\frac{2}{{{{\left( {x + 2} \right)}^2}}}\]

A.\[\frac{1}{6}\]

B. \[\frac{1}{{12}}\]

C. \[ - \frac{1}{6}\]

D. \[ - \frac{1}{{12}}\]

A.\[\{ 1\} \]

B. \[\mathbb{R} \setminus \left\{ 1 \right\}\]

C. \[\emptyset \]

D. R

A.\[y = \frac{{{x^3} + 1}}{x}\]

B. \[y = \frac{{3\left( {{x^2} + x} \right)}}{{{x^3}}}\]

C. \[y = \frac{{{x^3} + 5x - 1}}{x}\]

D. \[y = \frac{{2{x^2} + x - 1}}{x}\]

A.\[y' = - \frac{3}{{{x^4}}} + \frac{1}{{{x^3}}}\]

B. \[y' = \frac{{ - 3}}{{{x^4}}} + \frac{2}{{{x^3}}}\]

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

D. \[y' = \frac{3}{{{x^4}}} - \frac{1}{{{x^3}}}\]

A.\[\frac{a}{c}\]

B. \[\frac{{ad - bc}}{{{{\left( {cx + d} \right)}^2}}}\]

C. \[\frac{{ad + bc}}{{{{\left( {cx + d} \right)}^2}}}\]

D. \[\frac{{ad - bc}}{{cx + d}}\]Trả lời:

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

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

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

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

A.\[y' = \left( {{x^7} + x} \right)\left( {7{x^6} + 1} \right)\]

B.\[y' = 2\left( {{x^7} + x} \right)\]

C. \[y' = 2\left( {7{x^6} + 1} \right)\]

D. \[y' = 2\left( {{x^7} + x} \right)\left( {7{x^6} + 1} \right)\]

A.\[y' = \frac{3}{2}\frac{1}{{{x^2}\sqrt x }}\]

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

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

D. \[y' = - \frac{3}{2}\frac{1}{{{x^2}\sqrt x }}\]

A.\[y' = \cos 2x\]

B. \[ - \cos 2x\]

C. \[2\cos 2x\]

D. \[ - 2\cos 2x\]

A.\[y' = \frac{{ - 13{x^2} - 10x + 1}}{{{{\left( {{x^2} - 5x + 2} \right)}^2}}}\]

B. \[y' = \frac{{ - 13{x^2} + 5x + 11}}{{{{\left( {{x^2} - 5x + 2} \right)}^2}}}\]

C. \[y' = \frac{{ - 13{x^2} + 5x + 1}}{{{{\left( {{x^2} - 5x + 2} \right)}^2}}}\]

D. \[y' = \frac{{ - 13{x^2} + 10x + 1}}{{{{\left( {{x^2} - 5x + 2} \right)}^2}}}\]

A.0<x<2 

B.x<1           

C.x<0 hoặc x>1 

D.x<0 hoặc x>2

A.\[\frac{3}{2}\left( {\sqrt x + \frac{1}{{\sqrt x }} + \frac{1}{{x\sqrt x }} + \frac{1}{{{x^2}\sqrt x }}} \right)\]

B. \[x\sqrt x - 3\sqrt x + \frac{3}{{\sqrt x }} - \frac{1}{{x\sqrt x }}\]

C. \[\frac{3}{2}\left( { - \sqrt x + \frac{1}{{\sqrt x }} + \frac{1}{{x\sqrt x }} - \frac{1}{{{x^2}\sqrt x }}} \right)\]

D. \[\frac{3}{2}\left( {\sqrt x - \frac{1}{{\sqrt x }} - \frac{1}{{x\sqrt x }} + \frac{1}{{{x^2}\sqrt x }}} \right)\]

A.\[y' = 2\frac{{\tan x}}{{{{\cos }^2}x}} + 2\frac{{\cot x}}{{{{\sin }^2}x}}\]

B. \[y' = 2\frac{{\tan x}}{{{{\cos }^2}x}} - 2\frac{{\cot x}}{{{{\sin }^2}x}}\]

C.\[y' = 2\frac{{\tan x}}{{{{\sin }^2}x}} + 2\frac{{\cot x}}{{{{\cos }^2}x}}\]

D. \[y' = 2\tan x - 2\cot x\]

A.\[ - \sqrt 3 \]

B. 4

C. -3

D. \(\sqrt 3 \)

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

B. \[y' = {\tan ^3}\frac{x}{2}\]

C. \[y' = \frac{{\sin \frac{x}{2}}}{{co{s^3}\frac{x}{2}}}\]

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

A.\[y' = \sin x\left( { - 6{x^3} + 17{x^2} + 4x - 2} \right) + \cos x\left( {6{x^3} + 19{x^2} - 2} \right)\]

B. \[y' = \sin x\left( { - 6{x^3} + 17{x^2} + 4x - 2} \right) - \cos x\left( {6{x^3} + 19{x^2} - 2} \right)\]

C. \[y' = \sin x\left( {6{x^3} + 19{x^2} - 2} \right) + \cos x\left( { - 6{x^3} + 17{x^2} + 4x - 2} \right)\]

D. \[y' = \sin x\left( {6{x^3} + 19{x^2} - 2} \right) - \cos x\left( { - 6{x^3} + 17{x^2} + 4x - 2} \right)\]

A.\(f'\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{2x - 3\,\,khi\,x > 1}\\{2\,\,khi\,x \le 1}\end{array}} \right.\)

B.\(f'\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{2x - 3\,\,khi\,x > 1}\\{2\,khi\,x < 1}\end{array}} \right.\)

C. Không tồn tại đạo hàm  

D. \(f'\left( x \right) = 2x - 3\)

A.\[m \le \sqrt 2 \]

B. \[m \le 2\]

C. \[m \le 0\]

D. \(m < 0\)

A.\[(uv)' = u'v + v'u\]

B. \[(u + v)' = u' + v'\]

C. \[(u - v)' = u' - v'\]

D. \[{\left( {\frac{u}{v}} \right)^\prime } = \frac{{u'v + v'u}}{{{v^2}}}\]

A.\[1 + 2\sin x\]

B. \[1 + \sin 2x\]

C. \[1 + 2\cos x\]

D. \[2\cos x\]

A.\[y' = 50x - 1\]

B. \[y' = 50x - 10\]

C. \[y' = 10x - 5\]

D. \[y' = 10x - 1\]

A.\[ - \frac{1}{{{x^3}}}\]

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

C. \[ - \frac{2}{{{x^3}}}\]

D. \[ - \frac{1}{{{x^4}}}\]

A.\[3\sin x + 2\cos x\]

B. \[3\sin x - 2\cos x\]

C. \[ - 3\sin x - 2\cos x\]

D. \[ - 3\sin x + 2\cos x\]

A.x+2

B.2x+6

C.2x+6

D.4x+11

A.12

B.6

C.24

D.4

A.\[{\left( {\frac{1}{x}} \right)^\prime } = \frac{1}{{{x^2}}}\]

B. \[(\sqrt x )' = \frac{1}{{2\sqrt x }}\]  với x>0

C.\[{\left( {{x^n}} \right)^\prime } = n{x^{n - 1}}\]. với n nguyên dương

D.\[(c)' = 0\], với c hằng số

A.\[\frac{1}{{{{\sin }^2}x \cdot {{\cos }^2}x}}\]

B. \[ - \tan x + \cot x\]

C. \[\frac{{ - 1}}{{{{\sin }^2}x \cdot {{\cos }^2}x}}\]

D. 1

A.\[y' = \frac{{3x}}{{\sqrt {{x^2} + 1} }}\]

B. \[y' = \frac{{9{x^2} - x + 3}}{{\sqrt {{x^2} + 1} }}\]

C. \[y' = \frac{{9{x^2} - 2x + 3}}{{\sqrt {{x^2} + 1} }}\]

D. \[y' = \frac{{6{x^2} - x + 3}}{{\sqrt {{x^2} + 1} }}\]

D. \[ - \frac{3}{2}\]

A.−2018.    

B.2021.       

C.2021.     

D.2019

A.4

B.-2

C.3

D.2

A.27

B.43

C.5

D.26

A.33m/s

B.9m/s.

C.27m/s.

D.3m/s.

A.\[\frac{{3\cos 2x + 2\sin 2x + 1}}{{{{\left( {\cos 2x + 3} \right)}^2}}}\]

B. \[\frac{{2\left( {3\cos 2x + 2\sin 2x + 1} \right)}}{{{{\left( {\cos 2x + 3} \right)}^2}}}\]

C. \[\frac{{2\left( {3\cos 2x + 2\sin 2x + 1} \right)}}{{\cos 2x + 3}}\]

D. \[\frac{{3\cos 2x + 2\sin 2x + 1}}{{\cos 2x + 3}}\]

A. \[S = \left( {1;2} \right]\]

B. \[S = \left[ {1;2} \right)\]

C. \[S = \left( {1;2} \right)\]

D. \[S = \left[ {1;2} \right]\]

A.\[f'\left( 0 \right) = 0.\]

B. \[f'\left( 0 \right) = - 2018!.\]

C. \[f'\left( 0 \right) = 2018!.\]

D. \[f'\left( 0 \right) = 2018.\]