Trắc nghiệm Định nghĩa và ý nghĩa của đạo hàm Toán Lớp 11

A. (x2 – x + 1)2(x2 + x + 1)

B. (x2 – x + 1)2(x2 + x + 1)[(2x + 3)(x + x2)]

C. (x2 – x + 1)2(x2 + x + 1)[3(2x - 1) + 2(2x + 1)]

D. Tất cả sai

A. \(\frac{{2 - 4x + {x^2} + {x^3}}}{{{{\left( {1 + x + {x^2}} \right)}^2}}}\)

B. \(\frac{{2 - 4x + {x^2} + {x^3}}}{{{{\left( {1 - x + {x^2}} \right)}^2}}}\)

C. \(\frac{{2 - 4x - {x^2} + {x^3}}}{{{{\left( {1 - x + {x^2}} \right)}^2}}}\)

D. \(\frac{{2 - 4x + {x^2} - {x^3}}}{{{{\left( {1 - x + {x^2}} \right)}^2}}}\)

A. \(\left( { - \infty ; - \frac{1}{4}} \right]\)

B. \(\left( { - \infty ; - \frac{1}{4}} \right)\)

C. \(\left( { - \frac{1}{4}; + \infty } \right)\)

D. \(\left[ { - \frac{1}{4}; + \infty } \right)\)

A. \(\frac{{3x + 2}}{{3{x^2}}}\)

B. \(\frac{{ - 1}}{{{{\left( {x - 2} \right)}^2}}}\)

C. \(\frac{ 1}{{{{\left( {x - 2} \right)}^2}}}\)

D. \(\frac{{2x + 2}}{{{{\left( {{x^3} - 8} \right)}^2}}}\)

A. (2x + 1)(3x - 2)2

B. 2x2(3x - 2)2

C. (3x - 2)(24x2 + x - 2)

D. 2x(2x + 1)(3x - 2)

A. \(\frac{{2x}}{{{a^2} - {x^2}}}\)

B. \( \frac{{x\left( {2{a^2} - 3{x^2} - 1} \right)}}{{\left( {{a^2} - {x^2}} \right)\sqrt {{a^2} - {x^2}} }}\)

C. \(\frac{{2x}}{{\sqrt {2a - 2x} }}\)

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

A. \(6{x^2} - \frac{{3\sqrt x }}{2}\)

B. \(6{x^2} - \sqrt x \)

C. \(6{x^2} + \frac{{3\sqrt x }}{2}\)

D. \(6{x^2} + \sqrt x \)

A. \(5{\left( {{x^3} - \frac{4}{{\sqrt x }}} \right)^4}\)

B. \(5{\left( {{x^3} - \frac{4}{{\sqrt x }}} \right)^4}.\left( {3{x^2} -\frac{2}{{\sqrt x }}} \right)\)

C. \(5{\left( {{x^3} - \frac{4}{{\sqrt x }}} \right)^4}.\left( {3{x^2} -\frac{2}{{x\sqrt x }}} \right)\)

D. \(5{\left( {{x^3} - \frac{4}{{\sqrt x }}} \right)^4}.\left( {3{x^2} + \frac{2}{{x\sqrt x }}} \right)\)

A. \(3a^2- 6at - 15{t^2}\)

B. \(3a^2-3t^2\)

C. \(- 6at - 15{t^2}\)

D. \(3{a^2} - 3{t^2} - 6at - 15{t^2}\)

A. \(\frac{a}{{c + d}}\)

B. \(\frac{a}{{{{\left( {c + d} \right)}^2}}}\)

C. \(\frac{b}{{{{\left( {c + d} \right)}^2}}}\)

D. \(-\frac{a}{{c + d}}\)

A. \(\frac{{ - 2 - 6x}}{{{{\left( {3x - 2} \right)}^2}}}\)

B. \(\frac{{ - 2 - 6x}}{3}\)

C. \( \frac{{ - 9{x^2} + 12x - 11}}{{{{\left( {3x - 2} \right)}^2}}}\)

D. \(\frac{{ - 5 - 6x}}{{{{\left( {3x - 2} \right)}^2}}}\)

A. \(\frac{{19}}{{{{\left( {2x + 5} \right)}^2}}}\)

B. \(\frac{3}{{{{\left( {2x + 5} \right)}^2}}}\)

C. \(\frac{3}{2}\)

D. \(\frac{1}{{{{\left( {2x + 5} \right)}^2}}}\)

A. \( - 3 + {x^2} - x\)

B. \( - 3\left( {{x^2} + x} \right)\)

C. \( - 3 - {x^2} - x\)

D. \(- 4{x^3} + \frac{1}{2}{x^2} + 5x + 12\)

A. \(y'=\frac{4}{{\sqrt x }} - 5\)

B. \(y'= \frac{2}{{\sqrt x }} + \frac{5}{{{x^2}}}\)

C. \(y'= \frac{2}{{\sqrt x }} -\frac{5}{{{x^2}}}\)

D. \(y'= \frac{4}{{\sqrt x }} + \frac{5}{{{x^2}}}\)

A. \(\frac{ 3}{{{x^2}}} + \frac{2}{{{x^4}}} - \frac{7}{{{x^6}}} +\frac{6}{{{x^{10}}}}\)

B. \(\frac{{ - 3}}{{{x^2}}} - \frac{2}{{{x^4}}} + \frac{7}{{{x^6}}} - \frac{6}{{{x^{10}}}}\)

C. \(- \frac{3}{{{x^2}}} - \frac{4}{{{x^3}}} + \frac{{21}}{{{x^4}}} - \frac{{30}}{{{x^6}}}

D. \(3 + \frac{1}{x} - \frac{7}{{3{x^2}}} + \frac{6}{{5{x^4}}}\)

A. \(8{x^3} - 9{x^2} + x - \frac{3}{2}\)

B. \(8{x^3} + 9{x^2} + x - \frac{3}{2}\)

C. \(8{x^3} - 9{x^2} + x + \frac{3}{2}\)

D. \(8{x^3} - 9{x^2} - x - \frac{3}{2}\)

A. \(2x\frac{x}{{\sqrt {{x^2} + 2})}}\]

B. \(\frac{{4{x^2} - x + 4}}{{\sqrt {{x^2} + 2} }}\)

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

D. \(2 + \frac{x}{{\sqrt {{x^2} + 2} }}\)

A. \(y' = \left( {8{x^3} - 6x - 5} \right) . \left( {2x - 7} \right)\)

B. \( \left( {8{x^3} - 6x - 5} \right)\left( {{x^2} - 7x} \right) - \left( {2{x^4} - 3{x^2} - 5x} \right)\left( {2x - 7} \right)\)

C. \( \left( {8{x^3} - 6x - 5} \right)\left( {{x^2} - 7x} \right) + \left( {2{x^4} - 3{x^2} - 5x} \right)\left( {2x - 7} \right)\)

D. \(y' = \left( {8{x^3} - 6x - 5} \right) + \left( {2x - 7} \right)\)

A. \(5{x^4} - \frac{1}{{2\sqrt x }} + \frac{3}{{{x^2}}}\)

B. \({x^4} - \frac{1}{{\sqrt x }} - \frac{3}{{{x^2}}}\)

C. \(\frac{{4{x^4}}}{x} - \sqrt x  - \frac{3}{x}\)

D. \(\frac{1}{{25}}{x^4} - \frac{1}{{\sqrt x }} - \frac{3}{{{x^2}}}\)

A. 23

B. 7

C. - 7

D. - 23

A. \( \frac{{\sqrt {3\Delta x -2}  - 2}}{{\Delta x}}\)

B. \( \frac{{\sqrt {3\Delta x -6}  - 2}}{{\Delta x}}\)

C. \( \frac{{\sqrt {3\Delta x + 4}  - 2}}{{\Delta x}}\)  

D. \( \frac{{\sqrt {3\Delta x -2}  - 2}}{{\Delta x}}\)

A. (∆x)2+2∆x

B. (∆x)2+4∆x

C. (∆x)2+2∆x - 3

D. 3

A. - 1

B. 1

C. \(-\frac{1}{2}\)

D. \(\frac{1}{2}\)

A. y’ = 2x.cosx – x2sinx.

B. y’ = 2x.cosx + x2sinx.

C. y’ = 2x.sinx – x2cosx.

D. y’ = 2x.sinx + x2cosx.

A. y’ = sinx(3cos2x – 1).

B. y’ = sinx(3cos2x + 1).

C. y’ = sinx(cos2x + 1).

D. y’ = sinx(cos2x – 1).

A. \(\frac{1}{{{{\cos }^2}2x}}\)

B. \(\frac{4}{{{{\sin }^2}2x}}\)

C. \(\frac{4}{{{{\cos }^2}2x}}\)

D. \(\frac{1}{{{{\sin }^2}2x}}\)

A. \(x =  \frac{\pi }{2} + 2k\pi \)

B. \(x =  - \frac{\pi }{6} + k\pi \)

C. \(x =  - \frac{\pi }{6} + 2k\pi \)

D. Đáp án khác

A. \(\frac{{x\cos x - \sin x}}{{{x^2}}}\)

B. \(\frac{{x\sin x - \sin x}}{{{x^2}}}\)

C. \(\frac{{x\cos x - \cos x}}{{{x^2}}}\)

D. \(\frac{{\cos x - \sin x}}{{{x^2}}}\)

A. \(\frac{{ - \sin 2x}}{{\sqrt {\cos x} }}\)

B. \(\frac{{ - \sin 2x}}{{\sqrt {\cos 2x} }}\)

C. \(\frac{{ - \sin x}}{{\sqrt {\cos x} }}\)

D. \(\frac{{ \sin 2x}}{{\sqrt {\cos x} }}\)

A. \(\frac{{2\sin x}}{{{{\left( {\sin x - \cos x} \right)}^2}}}\)

B. \(\frac{{2\sin 2x}}{{{{\left( {\sin x - \cos x} \right)}^2}}}\)

C. \(\frac{{2\cos x}}{{{{\left( {\sin x - \cos x} \right)}^2}}}\)

D. \(\frac{{2\cos x}}{{\sin x - \cos x}}\)

A. cos 8x - cos 2x

B. 2 cos 8x - cos 2x

C. 4 cos 8x - cos2x

D. Đáp án khác

A. 2 cosx.sinx

B. -sin2 x

C. -sinx

D. Tất cả sai

A. \(\cos \sqrt x \)

B. \(\frac{{\cos \sqrt x }}{{2\sqrt x }}\)

C. \(\frac{{\cos \sqrt x }}{{\sqrt x }}\)

D. Đáp án khác

A. R \ {1}.

B. ∅.

C. (1; +∞).

D. R

A. ∅.

B. (-∞; 0).

C. (0; +∞).

D. (-∞; 0].

A. ∅.

B. (-∞; 0].

C. [0; +∞).

D. R

A. \(\left( { - \infty ; + \infty } \right)\)

B. \(\left( { - \infty ;\frac{1}{9}} \right)\)

C. \(\left( {\frac{1}{9}; + \infty } \right)\)

D. Ø

A. 0 < x < 2.

B. x < 1.

C. x < 0 hoặc x > 1

D. x < 0 hoặc x > 2.

A. \(\left\{ {0;\frac{2}{3}} \right\}\)

B. \(\left\{ {0;-\frac{2}{3}} \right\}\)

C. \(\left\{ {0;\frac{3}{2}} \right\}\)

D. \(\left\{ {0;-\frac{3}{2}} \right\}\)

A. {0}

B. 0

C. 4

D. - 2

A. \(\left[ { - \sqrt 3 ;\sqrt 3 } \right]\)

B. \(\left[ { - \frac{1}{{\sqrt 3 }};\frac{1}{{\sqrt 3 }}} \right]\)

C. \(\left[ { - \frac{1}{{\sqrt 3 }};\frac{1}{{\sqrt 3 }}} \right]\)

D. \(\left( { - \infty ; - \frac{1}{{\sqrt 3 }}} \right] \cup \left[ {\frac{1}{{\sqrt 3 }}; + \infty } \right)\)

A. \(\left\{ { - 2\sqrt 2 } \right\}\)

B. \(\left\{ {2;\sqrt 2 } \right\}\)

C. \(\left\{ { - 4\sqrt 2 } \right\}\)

D. \(\left\{ { 2\sqrt 2 } \right\}\)

A. {-1; 2}.

B. {-1; 3}.

C. {0; 4}.

D. {1; 2}.

A. \(\frac{{2{x^2} + 1}}{{2\sqrt {{x^2} + 1} }}\)

B. \(\frac{{{x^2} + 1}}{{\sqrt {{x^2} + 1} }}\)

C. \(\frac{{4{x^2} + 1}}{{\sqrt {{x^2} + 1} }}\)

D. \(\frac{{2{x^2} + 1}}{{\sqrt {{x^2} + 1} }}\)

A. \(\frac{{3x - 1}}{{\sqrt {3{x^2} - 2x + 1} }}\)

B. \(\frac{{6x - 2}}{{\sqrt {3{x^2} - 2x + 1} }}\)

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

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

A. \(\frac{7}{2}\sqrt {{x^5}}  - \frac{5}{{2\sqrt x }}\)

B. \(3{x^2} - \frac{1}{{2\sqrt x }}\)

C. \(3{x^2} - \frac{5}{{2\sqrt x }}\)

D. \(\frac{7}{2}\sqrt[5]{{{x^2}}} - \frac{5}{{2\sqrt x }}\)

A. \(y'=\frac{{3{x^2} - 6x}}{{\sqrt {{x^3} - 3{x^2} + 2} }}\)

B. \(y'=\frac{{3{x^2}+ 6x}}{{2\sqrt {{x^3} - 3{x^2} + 2} }}\)

C. \(y'=\frac{{3{x^2} - 6x}}{{2\sqrt {{x^3} - 3{x^2}- 2} }}\)

D. \(y'=\frac{{3{x^2} - 6x}}{{2\sqrt {{x^3} - 3{x^2} + 2} }}\)

A. \(- \frac{3}{{{x^4}}} + \frac{2}{{{x^3}}}\)

B. \(- \frac{3}{{{x^4}}} + \frac{1}{{{x^3}}}\)

C. \(- \frac{3}{{{x^4}}} - \frac{2}{{{x^3}}}\)

D. \(\frac{3}{{{x^4}}} - \frac{1}{{{x^3}}}\)

A. \(y = {x^2} - \frac{1}{x}\)

B. \(y = 2 - \frac{2}{{{x^3}}}\)

C. \(y = {x^2} + \frac{1}{x}\)

D. \(y = 2 - \frac{1}{x}\)

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

B. \(\frac{1}{{2x + 2}}\)

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

D. \( - \frac{4}{{{{\left( {{x^2} + 2x - 3} \right)}^2}}}\)