109 câu Trắc nghiệm Toán 11 Dạng 2: Tính đạo hàm bằng công thức có đáp án (Mới nhất)

A. \[y' = \sin x\].

B. \[y' = - \sin x\].

C. \[y' = - \cos x\].

D. \[y' = \frac{1}{{\sin x}}\].

A. \[y' = \cot x\].

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

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

D. \[y' = 1 - {\tan ^2}x\].

A. \[y' = - \tan x\].

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

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

D. \[y' = 1 + {\cot ^2}x\].

A. Hàm số \(y = \cos x\) có đạo hàm tại mọi điểm thuộc miền xác định của nó.

B. Hàm số \(y = \tan x\) có đạo hàm tại mọi điểm thuộc miền xác định của nó.

C. Hàm số \(y = \cot x\) có đạo hàm tại mọi điểm thuộc miền xác định của nó.

D. Hàm số \(y = \frac{1}{{\sin x}}\) có đạo hàm tại mọi điểm thuộc miền xác định của nó.

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

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

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

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

A.   

B. 

C.  

D.   

A. 

B. 

C. 

D. 

A. \[2\sin 8x\].

B. \[8\sin 8x\].

C. \[\sin 8x\].

D. \[4\sin 8x\].

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

B. \( - 4x\cos {x^2}\).

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

D. \( - 4x\sin {x^2}\).

A. \(x = - \frac{\pi }{3} + k2\pi \).

B. \(x = \frac{\pi }{3} + \frac{{k\pi }}{2}\).

C. \(x = - \frac{\pi }{3} + k\pi \).

D. \(x = - \frac{\pi }{3} + \frac{{k\pi }}{2}\).

A. \(\frac{{ - 3}}{{{{\sin }^2}3x}} + \frac{1}{{{{\cos }^2}2x}} \cdot \)

B. \(\frac{{ - 3}}{{{{\sin }^2}3x}} - \frac{1}{{{{\cos }^2}2x}} \cdot \)

C. \(\frac{{ - 3}}{{{{\sin }^2}3x}} - \frac{x}{{{{\cos }^2}2x}} \cdot \)

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

A. \[y' = 4\sin x + \sin 2x + 1.\]

B. \[y' = 4\sin 2x + 1.\]

C. \[y' = 1.\]

D. \[y' = 4\sin x - 2\sin 2x + 1.\]

A. 

B.   

C.     

D.  

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

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

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

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

A. \(x = \frac{\pi }{3} + k2\pi \).

B. \(x = \frac{\pi }{3} - k\pi \).

C. \(x = - \frac{\pi }{3} + k2\pi \).

D. \(x = - \frac{\pi }{3} + k\pi \).

A. \[y' = 1 + \tan x\].

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

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

D. \[y' = 1 + {\tan ^2}x\].

A. 

B. 

C. 

D. 

A. \[\frac{7}{{{{\cos }^2}7x}}\].

B. \[ - \frac{7}{{{{\cos }^2}7x}}\].

C. \[ - \frac{7}{{{{\sin }^2}7x}}\].

D. \[\frac{{7x}}{{{{\cos }^2}7x}}\].

A. \[4\cos 2x + 2\sin 2x\].

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

C. \[4\cos 2x - 2\sin 2x\].

D. \[ - 4\cos 2x - 2\sin 2x\].

A. \[ - 2\sin 2x\].

B. \[ - \cos \left( {\frac{\pi }{2} - 2x} \right)\].

C. \[2\sin 2x\].

D. \[\cos \left( {\frac{\pi }{2} - 2x} \right)\].

A. \[\frac{{3\cos 3x}}{{\sqrt {\sin 3x} }} \cdot \]

B. \[\frac{{3\cos 3x}}{{2\sqrt {\sin 3x} }} \cdot \]

C. \[ - \frac{{3\cos 3x}}{{2\sqrt {\sin 3x} }} \cdot \]

D. \[\frac{{\cos 3x}}{{2\sqrt {\sin 3x} }} \cdot \]

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

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

C. \(\frac{1}{2}x\sin \left( {\frac{\pi }{3} - x} \right)\).

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

A. \(\sin \left( {\tan x} \right) \cdot \frac{1}{{{{\cos }^2}x}} \cdot \)

B. \( - \sin \left( {\tan x} \right) \cdot \frac{1}{{{{\cos }^2}x}} \cdot \)

C. \[\sin \left( {\tan x} \right)\].

D. \[--\sin \left( {\tan x} \right)\].

A. \(y' = x\cos ({x^2} + 2)\)

B. \(y' = 4\cos ({x^2} + 2)\)

C. \(y' = 2x\cos ({x^2} + 2)\)

D. \(y' = 4x\cos ({x^2} + 2)\)

A. \[y' = {\mathop{\rm sinx}\nolimits} \left( {3{{\cos }^2}x - 1} \right)\].

B. \[y' = {\mathop{\rm sinx}\nolimits} \left( {3{{\cos }^2}x + 1} \right)\].

C. \[y' = {\mathop{\rm sinx}\nolimits} \left( {{{\cos }^2}x + 1} \right)\].

D. \[y' = {\mathop{\rm sinx}\nolimits} \left( {{{\cos }^2}x - 1} \right)\].

A. \(y' = \frac{{x\cos x + \sin x}}{{{x^2}}}\).

B. \(y' = \frac{{x\cos x - \sin x}}{{{x^2}}}\).

C. \(y' = \frac{{x\sin x + \cos x}}{{{x^2}}}\).

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

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

B. \(y' = \frac{{\sin x - x\cos x}}{{\sin x}}\)

C. \(y' = \frac{{\sin x + \cos x}}{{\sin x}}\)

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

A. \(y' = 2x.\cos x - {x^2}\sin x\).

B. \(y' = 2x.\cos x + {x^2}\sin x\).

C. \(y' = 2x.sinx - {x^2}\cos x\).

D. \(y' = 2x.\sin x + {x^2}\cos x\).

A. \[y' = \cos x - \sin x + 1\].

B. \[y' = \cos x + \sin x + \cos 2x\].

C. \[y' = \cos x - \sin x + \cos 2x\].

D. \[y' = \cos x + \sin x + 1\].

A. Cả hai đều sai.

B. Chỉ (II).

C. Chỉ (I).

D. Cả hai đều đúng.

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

B. \[y' = \frac{{ - 2\sin 2x\left( {3x + 1} \right) - 3\cos 2x}}{{3x + 1}}.\]

C. \[y' = \frac{{ - \sin 2x\left( {3x + 1} \right) - 3\cos 2x}}{{{{\left( {3x + 1} \right)}^2}}}.\]

D. \[y' = \frac{{2\sin 2x\left( {3x + 1} \right) + 3\cos 2x}}{{{{\left( {3x + 1} \right)}^2}}}.\]

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

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

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

D. \({\left( {\frac{x}{{\cos x + x\sin x}}} \right)^2}\)

A. \(\pi + k2\pi \).

B. \(2\pi + k4\pi \).

C. \(2\pi + k\pi \).

D. \(\pi + k\pi \).

A. \(y' = 2\cos \sqrt x \).

B. \(y' = \frac{1}{{\sqrt x }}\cos \sqrt x \).

C. \(y' = 2\sqrt x .\cos \frac{1}{{\sqrt x }}\).

D. \(y' = \frac{1}{{\sqrt x .\cos \sqrt x }}\).

A. \(y' = \frac{1}{{\sqrt {\sin x} }} - \frac{1}{{\sqrt {\cos x} }}\).

B. \(y' = \frac{1}{{\sqrt {\sin x} }} + \frac{1}{{\sqrt {\cos x} }}\).

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

D. \(y' = \frac{{\cos x}}{{\sqrt {\sin x} }} + \frac{{\sin x}}{{\sqrt {\cos x} }}\).

A. \(y' = \frac{{\sin \frac{x}{2}}}{{{{\cos }^3}\frac{x}{2}}}\).

B. \(y' = \frac{{2\sin \frac{x}{2}}}{{{{\cos }^3}\frac{x}{2}}}\).

C. \(y' = \frac{{\sin \frac{x}{2}}}{{2{{\cos }^3}\frac{x}{2}}}\).

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

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

B. \(12{\sin ^2}\left( {2x + 1} \right)\cos \left( {2x + 1} \right).\)

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

D. \(6{\sin ^2}\left( {2x + 1} \right)\cos \left( {2x + 1} \right).\)

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

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

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

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

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

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

C. \(\frac{2}{{2\sqrt {\sin x + 2x} }}.\)

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

A. \[y' = \sin 8x + \frac{{45}}{2}cos5x.\sin 10x\]

B. \(y' = 8\sin 8x + \frac{5}{2}cos5x.\sin 10x\)

C. \(y' = 8\sin x + \frac{{45}}{2}cos5x.\sin 10x\)

D. \(y' = 8\sin 8x + \frac{{45}}{2}cos5x.\sin 10x\)

A. \(y' = 6\sin 4x{\left( {2 + {{\sin }^2}2x} \right)^3}.\)

B. \(y' = 3\sin 4x{\left( {2 + {{\sin }^2}2x} \right)^2}.\)

C. \(y' = sin4x{\left( {2 + {{\sin }^2}2x} \right)^2}.\)

D. \(y' = 6\sin 4x{\left( {2 + {{\sin }^2}2x} \right)^2}.\)

A. Chỉ (I).

B. Chỉ (II).

C. Không cách nào.

D. Cả hai cách.

A. \[\frac{{\cos x}}{{2\sqrt {\cos x} }} \cdot \]

B. \[\frac{{ - \sin x}}{{2\sqrt {\cos x} }} \cdot \]

C. \[\frac{{\sin x}}{{2\sqrt {\cos x} }} \cdot \]

D. \[\frac{{ - \sin x}}{{\sqrt {\cos x} }} \cdot \]

A.

B.  

C.  

D.  

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

B. \(3{\left( {\sin x - cosx} \right)^2}\left( {\cos x - \sin x} \right).\)

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

D. \(3{\left( {\sin x + \cos x} \right)^2}\left( {\cos x - \sin x} \right).\)

A. \({\sin ^2}4x.\cos 4x.\)

B. \(\frac{3}{2}{\sin ^2}x.\cos x.\)

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

D. \(\frac{3}{2}{\sin ^2}4x.\cos 4x.\)

A. \( - 10{\cos ^4}2x.\)

B. \( - {\cos ^4}2x.\sin 2x.\) 

C. \( - 10{\cos ^4}2x.\sin x.\)

D. \( - 10{\cos ^4}2x.\sin 2x.\)

A. \(y' = \frac{{1 + {{\cot }^2}2x}}{{\sqrt {\cot 2x} }}\).

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

C. \(y' = \frac{{1 + {{\tan }^2}2x}}{{\sqrt {\cot 2x} }}\).

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

A. \(f\left( {\frac{\pi }{2}} \right) = - 1\).

B. \(f'\left( x \right) = \frac{{ - 2\sin 2x}}{{3.\sqrt[3]{{{{\cos }^2}2x}}}}\).

C. \(f'\left( {\frac{\pi }{2}} \right) = 1\).

D. \(3.{y^2}.y' + 2\sin 2x = 0\).

A.

B.  

C.  

D.  

A.

B.    

C.  

D.  

A. \(f'\left( {\frac{\pi }{2}} \right) = - 1\).

B. \[f'\left( x \right) = \frac{{ - 2\sin 2x}}{{3\sqrt[3]{{\cos 2x}}}} \cdot \]

C. \[3y.y' + 2\sin 2x = 0\].

D. \(f'\left( {\frac{\pi }{2}} \right) = 0\).

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

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

C. \[y' = 2\sin 4x.\cos x + \sin x.{\sin ^2}2x - \frac{1}{{x\sqrt x }} \cdot \]

D. \[y' = 2\sin 4x.\cos x - \sin x.{\sin ^2}2x - \frac{1}{{x\sqrt x }} \cdot \]

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

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

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

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

A. \[x + \frac{1}{2}\cos 2x\].

B. \(x - \frac{1}{2}\cos 2x\).

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

D. \[x + \;\sin 2x\].

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

B. \(\frac{{ - 4}}{{\sin \left( {1 - 2x} \right)}}\)

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

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

A. Chỉ \[\left( {{\rm{II}}} \right)\].

B. Chỉ \[\left( {\rm{I}} \right)\].

C. Cả hai đều sai.

D. Cả hai đều đúng.

A. \[y' = - 2\sin \left( {\pi - 4x} \right) + \frac{\pi }{2} \cdot \]

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

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

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

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

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

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

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

A. \[y' = - 2\cot \left( {\cos x} \right)\frac{1}{{{{\sin }^2}\left( {\cos x} \right)}} + \frac{{\cos x}}{{2\sqrt {\sin x - \frac{\pi }{2}} }}.\]

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

C. \[y' = - 2\cot \left( {\cos x} \right)\frac{1}{{{{\sin }^2}\left( {\cos x} \right)}} + \frac{{\cos x}}{{\sqrt {\sin x - \frac{\pi }{2}} }}.\]

D. \[y' = 2\cot \left( {\cos x} \right)\frac{1}{{{{\sin }^2}\left( {\cos x} \right)}}.\sin x + \frac{{\cos x}}{{\sqrt {\sin x - \frac{\pi }{2}} }}.\]

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

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

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

D. \[y' = 2x\tan x + \frac{{{x^2}}}{{{{\cos }^2}x}} + \frac{1}{{\sqrt x }}.\]

A. Chỉ (I).

B. Chỉ (II).

C. Không cách nào.

D. Cả hai đều đúng.

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

B. \( - \frac{{1 + {{\cos }^2}x}}{{2{{\sin }^3}x}}\).

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

D. \(\frac{{1 + {{\cos }^2}x}}{{2{{\sin }^3}x}}\).

A. \(\frac{{5 + 2{{\tan }^2}x}}{{2\sqrt {3x + 2\tan x} }}\)

B. \(\frac{{5 - 2{{\tan }^2}x}}{{2\sqrt {3x + 2\tan x} }}\)

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

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

A. \(3\sin (6x + 2)\)

B. \(\sin (6x + 2)\)

C. \( - 3\sin (6x + 2)\)

D. \(3\cos (6x + 2)\)

A. \(y' = \frac{{3\tan x(1 + {{\tan }^2}x) - (1 + {{\cot }^2}2x)}}{{3\sqrt {3{{\tan }^2}x + \cot 2x} }}\)

B. \(y' = \frac{{3\tan x(1 + {{\tan }^2}x) - (1 + {{\cot }^2}2x)}}{{2\sqrt {3{{\tan }^2}x + \cot 2x} }}\)

C. \(y' = \frac{{3\tan x(1 + {{\tan }^2}x) + (1 + {{\cot }^2}2x)}}{{\sqrt {3{{\tan }^2}x + \cot 2x} }}\)

D. \(y' = \frac{{3\tan x(1 + {{\tan }^2}x) - (1 + {{\cot }^2}2x)}}{{\sqrt {3{{\tan }^2}x + \cot 2x} }}\)

A. \(y' = \frac{{3{x^2} + 8{{\cos }^3}(2x - \frac{\pi }{4})\sin (2x - \frac{\pi }{4})}}{{3\sqrt[3]{{{{\left( {{x^3} + {{\cos }^4}(2x - \frac{\pi }{3})} \right)}^3}}}}}\)

B. \(y' = \frac{{3{x^2} - 8{{\cos }^3}(2x - \frac{\pi }{4})\sin (2x - \frac{\pi }{4})}}{{4\sqrt[3]{{{{\left( {{x^3} + {{\cos }^4}(2x - \frac{\pi }{3})} \right)}^3}}}}}\)

C. \(y' = \frac{{6{x^2} - 8{{\cos }^3}(2x - \frac{\pi }{4})\sin (2x - \frac{\pi }{4})}}{{3\sqrt[3]{{{{\left( {{x^3} + {{\cos }^4}(2x - \frac{\pi }{3})} \right)}^3}}}}}\)

D. \(y' = \frac{{3{x^2} - 8{{\cos }^3}(2x - \frac{\pi }{4})\sin (2x - \frac{\pi }{4})}}{{3\sqrt[3]{{{{\left( {{x^3} + {{\cos }^4}(2x - \frac{\pi }{3})} \right)}^3}}}}}\)

A. \(y' = - \sin (2{\sin ^3}x){\sin ^2}x\cos x\)

B. \(y' = - 6\sin (2{\sin ^3}x){\sin ^2}x\cos x\)

C. \(y' = - 7\sin (2{\sin ^3}x){\sin ^2}x\cos x\)

D. \(y' = - 3\sin (2{\sin ^3}x){\sin ^2}x\cos x\)

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

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

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

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

A. \(y' = \cos \left( {{{\cos }^2}x.{{\tan }^2}x} \right)\left( {\sin 2x{{\tan }^2}x + 2\tan x} \right)\)

B. \(y' = \cos \left( {{{\cos }^2}x.{{\tan }^2}x} \right)\left( {\sin 2x{{\tan }^2}x + \tan x} \right)\)

C. \(y' = \cos \left( {{{\cos }^2}x.{{\tan }^2}x} \right)\left( { - \sin 2x{{\tan }^2}x + \tan x} \right)\)

D. \(y' = \cos \left( {{{\cos }^2}x.{{\tan }^2}x} \right)\left( { - \sin 2x{{\tan }^2}x + 2\tan x} \right)\)

A. \(y' = \frac{1}{{\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}.\sin \left( {\frac{{\sqrt x + 1}}{{\sqrt x - 1}}} \right).\)

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

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

D. \(y' = \frac{1}{{\sqrt x {{\left( {\sqrt x - 1} \right)}^2}}}.\sin \left( {2.\frac{{\sqrt x + 1}}{{\sqrt x - 1}}} \right).\)

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

B. \(\frac{{ - 6}}{{{{\left( {\sin 2x - \cos 2x} \right)}^2}}}\)

C. \(\frac{6}{{{{\left( {2\sin 2x - \cos x} \right)}^2}}}\)

D. \(\frac{{ - 6}}{{{{\left( {2\sin 2x - \cos 2x} \right)}^2}}}\)

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

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

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

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

A. \(y' = \sin \left( {2\cos \left( {{{\tan }^4}3x} \right)} \right).\left( {\sin \left( {{{\tan }^4}3x} \right)} \right).4{\tan ^3}3x.\left( {1 + {{\tan }^3}3x} \right).3\)

B. \(y' = \sin \left( {2\cos \left( {{{\tan }^4}3x} \right)} \right).\left( {\sin \left( {{{\tan }^4}3x} \right)} \right).{\tan ^3}3x.\left( {1 + {{\tan }^3}3x} \right).\)

C. \(y' = \sin \left( {2\cos \left( {{{\tan }^4}3x} \right)} \right).\left( {\sin \left( {{{\tan }^4}3x} \right)} \right).4{\tan ^3}3x.\left( {1 + {{\tan }^3}3x} \right)\)

D. \(y' = - \sin \left( {2\cos \left( {{{\tan }^4}3x} \right)} \right).\left( {\sin \left( {{{\tan }^4}3x} \right)} \right).4{\tan ^3}3x.\left( {1 + {{\tan }^3}3x} \right).3\)

A. \(y' = {\cot ^3}x - 1\)

B. \(y' = 3{\cot ^4}x - 1\)

C. \(y' = {\cot ^4}x - 1\)

D. \(y' = {\cot ^4}x\)

A. \(y' = 12{\sin ^2}2x\cos 2x + 6\tan 3x\left( {1 + 2{{\tan }^2}3x} \right) + \cos 4x - 4x\sin 4x\)

B. \(y' = 12{\sin ^2}2x\cos 2x + 6\tan 3x\left( {1 + {{\tan }^2}3x} \right) + \cos 4x - x\sin 4x\)

C. \(y' = 12{\sin ^2}2x\cos 2x + \tan 3x\left( {1 - {{\tan }^2}3x} \right) + \cos 4x - 4x\sin 4x\)

D. \(y' = 12{\sin ^2}2x\cos 2x + 6\tan 3x\left( {1 + {{\tan }^2}3x} \right) + \cos 4x - 4x\sin 4x\)

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

B. \(y' = \frac{{2x\cos 2x + \sin 2x}}{{{x^2}}} + \frac{{\cos 3x + 3x\sin 3x}}{{{{\cos }^2}3x}}\)

C. \(y' = \frac{{2x\cos 2x - \sin 2x}}{{{x^2}}} - \frac{{\cos 3x + 3x\sin 3x}}{{{{\cos }^2}3x}}\)

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

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

B. \(y' = \frac{{2x\cos 2x + \sin 2x}}{{{x^2}}} + \frac{{\cos 3x + 3x\sin 3x}}{{{{\cos }^2}3x}}\)

C. \(y' = \frac{{2x\cos 2x - \sin 2x}}{{{x^2}}} - \frac{{\cos 3x + 3x\sin 3x}}{{{{\cos }^2}3x}}\)

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

A. \(y' = \sin 2x - 2x\cos 2x + \frac{{3{x^2} + 2x}}{{2\sqrt {{x^3} + {x^2} + 1} }}\)

B. \(y' = \sin 2x + 2x\cos 2x + \frac{{3{x^2} + 2x}}{{\sqrt {{x^3} + {x^2} + 1} }}\)

C. \(y' = \sin 2x + 2x\cos 2x - \frac{{3{x^2} + 2x}}{{2\sqrt {{x^3} + {x^2} + 1} }}\)

D. \(y' = \sin 2x + 2x\cos 2x + \frac{{3{x^2} + 2x}}{{2\sqrt {{x^3} + {x^2} + 1} }}\)

A. \(y' = \frac{{2\sin 2x + 3{x^2}}}{{\sqrt {2{{\sin }^2}x + {x^3} + 1} }}\)

B. \(y' = \frac{{2\sin 2x + 3{x^2}}}{{2\sqrt {2{{\sin }^2}x + {x^3} + 1} }}\)

C. \(y' = \frac{{\sin 2x + 3{x^2}}}{{\sqrt {2{{\sin }^2}x + {x^3} + 1} }}\)

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

A. \(y' = \tan 2x - 2x\left( {1 + {{\tan }^2}2x} \right) + \tan x + (x + 1)({\tan ^2} + 1)\)

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

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

D. \(y' = \tan 2x + 2x\left( {1 + {{\tan }^2}2x} \right) + \tan x + (x + 1)({\tan ^2} + 1)\)

A. \(y' = \frac{{3{{\sin }^2}\left( {2x - \frac{\pi }{3}} \right)\cos \left( {2x - \frac{\pi }{3}} \right)}}{{2\sqrt {{{\sin }^3}\left( {2x - \frac{\pi }{3}} \right) + 1} }}\)

B. \(y' = \frac{{{{\sin }^2}\left( {2x - \frac{\pi }{3}} \right)\cos \left( {2x - \frac{\pi }{3}} \right)}}{{2\sqrt {{{\sin }^3}\left( {2x - \frac{\pi }{3}} \right) + 1} }}\)

C. \(y' = \frac{{{{\sin }^2}\left( {2x - \frac{\pi }{3}} \right)\cos \left( {2x - \frac{\pi }{3}} \right)}}{{\sqrt {{{\sin }^3}\left( {2x - \frac{\pi }{3}} \right) + 1} }}\)

D. \(y' = \frac{{3{{\sin }^2}\left( {2x - \frac{\pi }{3}} \right)\cos \left( {2x - \frac{\pi }{3}} \right)}}{{\sqrt {{{\sin }^3}\left( {2x - \frac{\pi }{3}} \right) + 1} }}\)

A. Hàm số \[f\] không có đạo hàm tại \[{x_0} = 0\].

B. Hàm số \[f\] không liên tục tại \[{x_0} = 0\].

C. \[f'\left( {\frac{\pi }{2}} \right) = 0\].

D. \[f\left( {\frac{\pi }{2}} \right) = 1\].

A. \(f'(x) = \left\{ \begin{array}{l}{x^2}\sin \frac{1}{x} - x\cos \frac{1}{x}{\rm{   khi }}x \ne 0\\{\rm{0     khi   }}x = 0\end{array} \right.\)

B. \(f'(x) = \left\{ \begin{array}{l}3{x^2}\sin \frac{1}{x} - x\cos \frac{1}{x}{\rm{   khi }}x \ne 0\\0{\rm{     khi   }}x = 0\end{array} \right.\)

C. \(f'(x) = \left\{ \begin{array}{l}3{x^2}\sin \frac{1}{x} + x\cos \frac{1}{x}{\rm{   khi }}x \ne 0\\0{\rm{     khi   }}x = 0\end{array} \right.\)

D. \(f'(x) = \left\{ \begin{array}{l}3{x^2}\sin \frac{1}{x} - \cos \frac{1}{x}{\rm{   khi }}x \ne 0\\0{\rm{     khi   }}x = 0\end{array} \right.\)