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