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. \(m < 0\)