Trắc nghiệm Quy tắc tính đạo hàm Toán Lớp 11

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

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

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

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

A. \(y' = \frac{1}{{x\ln 10.{{\lg }^2}x}}\)

B. \(y' = - \frac{{\ln 10}}{{x.{{\lg }^2}x}}\)

C. \(y' = - \frac{1}{{x.{{\lg }^2}x}}\)

D. \(y' = - \frac{1}{{x.\ln 10{{\lg }^2}x}}\)

A. 2

B. 3

C. 4

D. 5

A. \(\frac{\pi }{3} + k2\pi {\mkern 1mu} {\mkern 1mu} \left( {k \in Z} \right)\)

B. \( - \frac{\pi }{3} + k2\pi {\mkern 1mu} {\mkern 1mu} \left( {k \in Z} \right)\)

C. \(\frac{\pi }{2} + k2\pi {\mkern 1mu} {\mkern 1mu} \left( {k \in Z} \right)\)

D. \(-\frac{\pi }{2} + k2\pi {\mkern 1mu} {\mkern 1mu} \left( {k \in Z} \right)\)

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

B. \(2 y+y^{\prime} \tan x+y^{\prime \prime}-2=0\)

C. \(2 y+y^{\prime} \tan x+y^{\prime \prime}-2=\pi\)

D. \(2 y+y^{\prime} \tan x+y^{\prime \prime}-2=-3\)

A. \(x=\frac{3\pi}{2}+k \frac{\pi}{2}(k \in \mathbb{Z})\)

B. \(x=\pi +k \frac{\pi}{2}(k \in \mathbb{Z})\)

C. \(x=\frac{\pi}{6}+k \frac{\pi}{2}(k \in \mathbb{Z})\)

D. \(x=k \frac{\pi}{2}(k \in \mathbb{Z})\)

A. \( y^{\prime}-\tan ^{2}\left(x-\frac{\pi}{4}\right)=0\)

B. \( y^{\prime}-\tan ^{2}\left(x-\frac{\pi}{4}\right)=1\)

C. \( y^{\prime}-\tan ^{2}\left(x-\frac{\pi}{4}\right)=\pi\)

D. \( y^{\prime}-\tan ^{2}\left(x-\frac{\pi}{4}\right)=-1\)

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

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

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

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

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

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

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

D. \(-(x-2)^{2} \sin (x+1)^{3} \text {. }\)

A. \(-\sin ^{2}(2 x+1)(\sin (2 x+1)+6 x \cos (2 x+1)) \text {. }\)

B. \(\sin ^{2}(2 x-1)(\sin (2 x+1)+6 x \cos (2 x+1)) \text {. }\)

C. \(\sin ^{2}(2 x+1)(\sin (2 x+1)+6 x \cos (2 x+1)) \text {. }\)

D. \(\frac{1}{2}\sin ^{2}(2 x+1)(\sin (2 x+1)+6 x \cos (2 x+1)) \text {. }\)

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

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

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

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

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

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

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

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

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

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

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

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

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

B. \( y^{\prime}=\cos 2 x-1\)

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

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

A. \(5 \cos 2 x-5 \cos x+9 \sin x .\)

B. \( \cos 2 x-5 \cos x+ \sin x .\)

C. \(15 \cos 2 x-5 \cos x+9 \sin x .\)

D. \(- \cos 2 x- \cos x+9 \sin x .\)

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

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

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

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

A. \(-5\left(4-\sin ^{2} 3 x\right)^{4} \cdot \sin 6 x\)

B. \(-\frac{2}{3}\left(4-\sin ^{2} 3 x\right)^{4} \cdot \sin 6 x\)

C. \(5\left(4-\sin ^{2} 3 x\right)^{4} \cdot \sin 6 x\)

D. \(-15\left(4-\sin ^{2} 3 x\right)^{4} \cdot \sin 6 x\)

A. \( x \cos x-\left(4 x^{2}-3\right) \sin x\)

B. \(8 x \cos x-\left(4 x^{2}-3\right) \sin x\)

C. \(-3 x \cos x-\left(4 x^{2}-3\right) \sin x\)

D. \(-2x \cos x-\left(4 x^{2}-3\right) \sin x\)

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

B. \(-\frac{5 \sin 2 \sqrt{1-3 x}}{2 \sqrt{1-3 x}}\)

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

D. \(-\frac{7 \sin 2 \sqrt{1-3 x}}{2 \sqrt{1-3 x}}\)

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

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

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

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

A. \(\frac{\sqrt 2}{3} .\)

B. \(\frac{1}{3} .\)

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

D. \(\frac{-2}{3} .\)

A. \(\pi\)

B. 0

C. 1

D. \(\sqrt 2\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A. \(6 \tan ^{2}\left(2 x-\frac{\pi}{4}\right)\left[1-\tan ^{2}\left(2 x-\frac{\pi}{4}\right)\right]\)

B. \(\tan \left(2 x-\frac{\pi}{4}\right)\left[1+\tan ^{2}\left(2 x-\frac{\pi}{4}\right)\right]\)

C. \(6 \tan ^{2}\left(2 x-\frac{\pi}{4}\right)\left[1+\tan ^{2}\left(2 x-\frac{\pi}{4}\right)\right]\)

D. \( \tan ^{2}\left(2 x-\frac{\pi}{4}\right)\left[1+\tan ^{2}\left(2 x-\frac{\pi}{4}\right)\right]\)

A. \(-12 \tan x\left(3-2 \tan ^{2} x\right)\left(1+\tan ^{2} x\right) . \)

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

C. \(-12 \tan x\left(1-2 \tan ^{2} x\right)\left(1+\tan ^{2} x\right) . \)

D. \(-5 \tan x\left(3-2 \tan ^{2} x\right)\left(1+\tan ^{2} x\right) . \)

A. \(1-\sin 4 x\)

B. \(2 \sin 4 x-1\)

C. \(2 \sin 4 x\)

D. \(2 \sin 4 x-\cos4x\)

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

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

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

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

A. \(x=1\)

B. \(x=\sqrt{2}, x=-\sqrt{2}\)

C. \(x=0;x=-1\)

D. \(x=\sqrt{2}\)

A. \(\frac{2 x^{4}- x^{3}+10 x^{2}-4}{\left(x^{2}+x+1\right)^{2}} \text {. }\)

B. \(\frac{4 x^{3}+10 x^{2}-4}{\left(x^{2}+x+1\right)^{2}} \text {. }\)

C. \(\frac{- x^{3}+10 x^{2}-4}{\left(x^{2}+x+1\right)^{2}} \text {. }\)

D. \(\frac{2 x^{4}+4 x^{3}+10 x^{2}-4}{\left(x^{2}+x+1\right)^{2}} \text {. }\)

A. \(-3x^{5}-2 x^{4}-x^{3}+2 x^{2}+4 x+2 \text {. }\)

B. \(3x^{5}-2 x^{4}-x^{3}+2 x^{2}+4 x+2 \text {. }\)

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

D. \(-x^{5}-2 x^{4}-x^{3}+2 x^{2}+4 x+2 \text {. }\)

A. \(S=\left(\frac{-1}{2} ; \frac{2}{3}\right]\)

B. \(S=\left(\frac{1}{2} ; \frac{2}{3}\right]\)

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

D. \(S=\left(\frac{1}{2} ; \frac{2}{3}\right)\)

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

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

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

D. \(x = \frac{{1\sqrt 3 }}{3}\)

A. \(\frac{-11 x+21}{\left(x^{2}-6 x+5\right) \sqrt{x^{2}-6 x+5}}\)

B. \(\frac{- x+21}{\left(x^{2}-6 x+5\right) \sqrt{x^{2}-6 x+5}}\)

C. \(\frac{-9 x+1}{\left(x^{2}-6 x+5\right) \sqrt{x^{2}-6 x+5}}\)

D. \(\frac{-2 x+21}{\left(x^{2}-6 x+5\right) \sqrt{x^{2}-6 x+5}}\)

A. \(x>\frac{5}{3} \text { hoặc } x<1 \text {. }\)

B. \(x>\frac{1}{3}\)

C. \(x>\frac{5}{3} \text { hoặc } x<-1 \text {. }\)

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

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

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

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

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

A. \(-(2 x-1)\left(-3 x^{2}+3 x-7\right)^{14} . \)

B. \(-45(2 x-1)\left(-3 x^{2}+3 x-7\right)^{13} . \)

C. \(-(2 x-1)\left( x^{2}+3 x-7\right)^{14} . \)

D. \(-45(2 x-1)\left(-3 x^{2}+3 x-7\right)^{14} . \)

A. \(\frac{2 x^{2}+8 x-11}{(x+2)^{2}} \)

B. \(\frac{ x^{2}+8 x-11}{(x+2)^{2}} \)

C. \(\frac{ x^{2}+8 x-1}{(x+2)^{2}} \)

D. \(\frac{2 x^{2}- x-11}{(x+2)^{2}} \)

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

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

C. \(5 x^{3}+4 x^{2}-1 \)

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

A. \(\frac{2 x^{2}-4 x+6}{\sqrt{x^{2}-2 x+5}}\)

B. \(-\frac{2 x^{2}-4 x+6}{\sqrt{x^{2}-2 x+5}}\)

C. \(-\frac{x^{2}-4 x+6}{2\sqrt{x^{2}-2 x+5}}\)

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

A. \(2015\left(\frac{2 x+1}{3 x+1}\right)^{2014} \frac{-1}{(3 x+1)^{2}}\)

B. \(\left(\frac{2 x+1}{3 x+1}\right)^{2014} \frac{-1}{(3 x+1)^{2}}\)

C. \(-2015\left(\frac{2 x+1}{3 x+1}\right)^{2014} \)

D. \(2015\left(\frac{2 x+1}{3 x+1}\right)^{2014}\)

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

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

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

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

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

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

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

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

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

B. \(10 x^{4}+6 x^{2}+4 x\)

C. \(-x^{4}+6 x^{2}+4 x+1\)

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

A. \(\frac{x^{2}+10 x-7}{(x+5)^{2}} .\)

B. \(\frac{3x^{2}+10 x-7}{(x+5)^{2}} .\)

C. \(\frac{-2x^{2}+ x-7}{(x+5)^{2}} .\)

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

A. \(15 x^{4}+\frac{12 x^{2}}{x^{6}}-2 \sqrt{x}+\frac{(2 x+1)}{2 \sqrt{x}}\)

B. \(-3 x^{4}+\frac{12 x^{2}}{x^{6}}+2 \sqrt{x}+\frac{(2 x+1)}{2 \sqrt{x}}\)

C. \(15 x^{4}+\frac{12 x^{2}}{x^{6}}+2 \sqrt{x}+\frac{(2 x+1)}{2 \sqrt{x}}\)

D. \( x^{4}+\frac{12 x^{2}}{x^{6}}+2 \sqrt{x}+\frac{(2 x+1)}{2 \sqrt{x}}\)

A. 1214

B. 4030

C. -2014

D. -1312

A. \((2 x+1)^{2}\left(10 x^{2}-14 x+16\right) . \)

B. \(( x+1)^{2}\left(10 x^{2}-14 x+16\right) .\)

C. \((2 x-1)^{2}\left( x^{2}-14 x+16\right) . \)

D. \(( x+1)^{2}\left( x^{2}-14 x+16\right) .\)