Trắc nghiệm Quy tắc tính đạo hàm Toán Lớp 11

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

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

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

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

A. $\frac{ x^{2}-12 x+11}{(x-3)^{2}}$

B. $\frac{2 x^{2}-12 x+11}{(x-3)^{2}}$

C. $\frac{2 x^{2}-12 x}{(x-3)^{2}}$

D. $\frac{ x^{2}-3x+11}{(x-3)^{2}}$

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

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

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

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

A. $\frac{4 m^{2}}{(x+m)^{2}}$

B. $\frac{-3 m^{2}}{(x+m)^{2}}$

C. $\frac{ m^{2}}{(x+m)^{2}}$

D. $\frac{3 m^{2}}{(x+m)^{2}}$

A. $\frac{-m^{2}+2m+2}{(x-m+1)^{2}} .$

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

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

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

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

B. $\frac{13}{(x+2)^{2}} .$

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

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

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

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

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

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

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

B. $\frac{5}{(1-4 x)^{2}}$

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

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

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

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

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

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

A. $31(1-2 x)\left(x-x^{2}\right)^{30}$

B. $31(1-2 x)\left(x-x^{2}\right)^{31}$

C. $-32(1-2 x)\left(x-x^{2}\right)^{31}$

D. $32(1-2 x)\left(x-x^{2}\right)^{31}$

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

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

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

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

A. $-48 x^{5}+48 x^{3}-12 x$

B. $21 x^{5}+48 x^{3}-12 x$

C. $-6 x^{5}+48 x^{3}-12 x$

D. $-12 x^{5}+48 x^{3}-12 x$

A. $-2 x^{3}+4 x .$

B. $-3 x^{3}+4 x .$

C. $-12 x^{3}+4 x .$

D. $- x^{3}+4 x .$

A. $-4x^{3}+2 x^{2}+13x-6$

B. $-4x^{3}+3 x^{2}+18 x-6$

C. $-x^{3}+2 x^{2}+18 x-6$

D. $8 x^{3}-12 x^{2}+18 x-6$

A. $-2 x^{5}-15 x^{4}-8 x+6 .$

B. $-6 x^{5}-5 x^{4}-8 x+6 .$

C. $12 x^{5}-15 x^{4}-8 x+6 .$

D. $-6 x^{5}-15 x^{4}-8 x.$

A. $15 x^{4}-24 m x^{3}-2 m \text {. }$

B. $-3 x^{4}-24 m x^{3}-2 m \text {. }$

C. $5 x^{4}-2 m x^{3}-2 m \text {. }$

D. $2 x^{4}-24 m x^{3}- m \text {. }$

A. $-3 m^{2} x^{3}-2(m-1) x \text {. }$

B. $4 m^{2} x^{3}-2(m-1) x \text {. }$

C. $m^{2} x^{3}-2(m-1) x \text {. }$

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

A. $-2x^{3}-4 x$

B. $-3x^{3}-4 x$

C. $x^{3}+4 x$

D. $-x^{3}-4 x$

A. $-4x^{3}-x$

B. $-3x^{3}-x$

C. $x^{3}-x$

D. $4x^{3}-x$

A. $6 x^{5}-6 x^{2}-10 x \text {. }$

B. $6 x^{5}-6 x^{2}+10 x \text {. }$

C. $3x^{5}-6 x^{2}+ x \text {. }$

D. $3 x^{5}-6 x^{2}-10 x \text {. }$

A. $x=\frac{\pi}{2}+k 2 \pi, x=-\frac{\pi}{6}+k 2 \pi, x=\frac{7 \pi}{6}+k 2 \pi$

B. $x=\frac{\pi}{2}+k 2 \pi, x=\pm\frac{\pi}{6}+k 2 \pi, x=\frac{7 \pi}{6}+k 2 \pi$

C. $x=\frac{\pi}{2}+k 2 \pi, x=-\frac{\pi}{6}+k 2 \pi$

D. $x=\frac{\pi}{2}+k \pi, x=-\frac{\pi}{6}+k \pi, x=\frac{7 \pi}{6}+k \pi$

A. $f^{\prime}\left(\frac{\pi}{4}\right)=\sqrt{2}$

B. $f^{\prime}\left(\frac{\pi}{4}\right)=\sqrt{2}-2$

C. $f^{\prime}\left(\frac{\pi}{4}\right)=\sqrt{2}-1$

D. $f^{\prime}\left(\frac{\pi}{4}\right)=-\sqrt{2}-2$

A. $f^{\prime}\left(\frac{\pi}{2}\right)=0$

B. $f^{\prime}\left(\frac{\pi}{2}\right)=-1$

C. $f^{\prime}\left(\frac{\pi}{2}\right)=-\frac{1}{2}$

D. $f^{\prime}\left(\frac{\pi}{2}\right)=-\frac{\sqrt 3}{2}$

A. 0

B. 1

C. -1

D. -1

A. 1

B. -1

C. 2

D. -2

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

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

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

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

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

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

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

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

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

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

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

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

A. $\frac{-x(4+3 \sin x)-3 \cos x\left(5 x^{2}+1\right)}{(4+3 \sin x)^{2}} \text {. }$

B. $\frac{10 x(4+3 \sin x)-3 \cos x\left(5 x^{2}+1\right)}{(4+3 \sin x)^{2}} \text {. }$

C. $\frac{10 x(4+3 \sin x)+ \cos x\left(5 x^{2}+1\right)}{(4+3 \sin x)^{2}} \text {. }$

D. $\frac{10 x(4-3 \sin x)-3 \cos x\left(5 x^{2}+1\right)}{(4+3 \sin x)^{2}} \text {. }$

A. $-\sin 2 x$

B. $-\cos 2 x+x$

C. $-\sin 2 x+x$

D. $-\cos 2 x$

A. $-\frac{\cos x}{x}+\frac{\sin x}{x^{2}}+\frac{1-x \cot x}{\sin x} \text {. }$

B. $\frac{\cos x}{x}-\frac{\sin x}{x^{2}}+\frac{x \cot x}{\sin x} \text {. }$

C. $\frac{\cos x}{x}-\frac{\sin x}{x^{2}}+\frac{1-x \cot x}{\sin x} \text {. }$

D. $\frac{\cos x}{x}+\frac{\sin x}{x^{2}}+\frac{1-x \cot x}{\sin x} \text {. }$

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

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

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

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

A. $\frac{\cos x+x \sin x}{\cos ^{2} x} \text {. }$

B. $-\frac{\cos x+x \sin x}{\cos ^{2} x} \text {. }$

C. $\frac{\cos x-x \sin x}{\cos ^{2} x} \text {. }$

D. $\frac{\cos x+ \sin x}{\cos ^{2} x} \text {. }$

A. $\frac{5 \cos 5 x}{2 \sqrt{2 x^{3}+\sin 5 x}}$

B. $\frac{6 x^{2}-5 \cos 5 x}{2 \sqrt{2 x^{3}+\sin 5 x}}$

C. $\frac{6 x^{2}+5 \cos 5 x}{2 \sqrt{2 x^{3}+\sin 5 x}}$

D. $\frac{ x^{2}+5 \cos 5 x}{2 \sqrt{2 x^{3}+\sin 5 x}}$

A. $\frac{2x \cos \sqrt{x^{2}+1}}{\sqrt{x^{2}+1}}$

B. $\frac{2x- \cos \sqrt{x^{2}+1}}{\sqrt{x^{2}+1}}$

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

D. $\frac{x- \cos \sqrt{x^{2}+1}}{\sqrt{x^{2}+1}}$

A. $\frac{x +\sin \sqrt{2+x^{2}}}{\sqrt{2+x^{2}}} .$

B. $\frac{x \sin \sqrt{2+x^{2}}}{\sqrt{2+x^{2}}} .$

C. $\frac{x^2 \sin \sqrt{2+x^{2}}}{\sqrt{2+x^{2}}} .$

D. $\frac{x- \sin \sqrt{2+x^{2}}}{\sqrt{2+x^{2}}} .$

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

B. $-\frac{\cos x+2}{2 \sqrt{\sin x+2 x}} .$

C. $\frac{\cos x}{ \sqrt{\sin x+2 x}} .$

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

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

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

C. $-\frac{3\sin 2 x}{\sqrt{\cos 2 x}} .$

D. $-\frac{2\sin 2 x}{\sqrt{\cos 2 x}} .$

A. $-\frac{\cos \sqrt{x}}{2 \sqrt{x}}.$

B. $\frac{\cos \sqrt{x}}{ \sqrt{x}}.$

C. $\frac{\cos \sqrt{x}}{2 \sqrt{x}}.$

D. $-\frac{\cos \sqrt{x}}{ \sqrt{x}}.$

A. $-3 \sin 4 x.$

B. $-5 \sin 4 x.$

C. $-4 \sin 4 x.$

D. $-2 \sin 4 x.$

A. $-2 \sin 4 x \cdot\left(2+\sin ^{2} 2 x\right)^{7}.$

B. $16 \sin 4 x \cdot\left(2+\sin ^{2} 2 x\right)^{7}.$

C. $8\sin 4 x \cdot\left(2+\sin ^{2} 2 x\right)^{7}.$

D. $-8\sin 4 x \cdot\left(2+\sin ^{2} 2 x\right)^{7}.$

A. $4(2 \cos x+\sin x)(2 \sin x-\cos x)^{3}.$

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

C. $-2(2 \cos x+\sin x)(2 \sin x-\cos x)^{3}.$

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

A. $- \cos \left(x+\frac{\pi}{4}\right) \cdot \sin ^{7}\left(x+\frac{\pi}{4}\right).$

B. $-12 \cos \left(x+\frac{\pi}{4}\right) \cdot \sin ^{7}\left(x+\frac{\pi}{4}\right).$

C. $128 \cos \left(x+\frac{\pi}{4}\right) \cdot \sin ^{8}\left(x+\frac{\pi}{4}\right).$

D. $128 \cos \left(x+\frac{\pi}{4}\right) \cdot \sin ^{7}\left(x+\frac{\pi}{4}\right).$

A. $- \cos x \cdot(3-\sin x)^{2} .$

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

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

D. $\cos x \cdot(3-\sin x)^{2} .$

A. $-12\left(2 x-\frac{\pi}{4}\right) \cdot \frac{\tan ^{2}\left(\frac{\pi}{4}-2 x\right)^{2}}{\cos ^{2}\left(\frac{\pi}{4}-2 x\right)^{2}} .$

B. $-6\left(2 x-\frac{\pi}{4}\right) \cdot \frac{\tan ^{2}\left(\frac{\pi}{4}-2 x\right)^{2}}{\cos ^{2}\left(\frac{\pi}{4}-2 x\right)^{2}} .$

C. $-2\left(2 x-\frac{\pi}{4}\right) \cdot \frac{\tan ^{2}\left(\frac{\pi}{4}-2 x\right)^{2}}{\cos ^{2}\left(\frac{\pi}{4}-2 x\right)^{2}} .$

D. $12\left(2 x-\frac{\pi}{4}\right) \cdot \frac{\tan ^{2}\left(\frac{\pi}{4}-2 x\right)^{2}}{\cos ^{2}\left(\frac{\pi}{4}-2 x\right)^{2}} .$

A. $-6015 x^{2} \cdot \cos ^{2016}\left(x^{3}+\frac{\pi}{7}\right) \cdot \sin \left(x^{3}+\frac{\pi}{7}\right)$

B. $-2017 x^{2} \cdot \cos ^{2016}\left(x^{3}+\frac{\pi}{7}\right) \cdot \sin \left(x^{3}+\frac{\pi}{7}\right)$

C. $6015 x^{2} \cdot \cos ^{2016}\left(x^{3}+\frac{\pi}{7}\right) \cdot \sin \left(x^{3}+\frac{\pi}{7}\right)$

D. $2017 x^{2} \cdot \cos ^{2016}\left(x^{3}+\frac{\pi}{7}\right) \cdot \sin \left(x^{3}+\frac{\pi}{7}\right)$

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

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

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

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

A. $8 \sin 8 x-9 \cos ^{2} 5 x \sin 5 x$

B. $\sin 8 x+45 \cos ^{2} 5 x \sin 5 x$

C. $8 \sin 8 x+45 \cos ^{2} 5 x \sin 5 x$

D. $8 \sin 8 x-45 \cos ^{2} 5 x \sin 5 x$

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

B. $\sin 2 x \cdot \cos \left(\sin ^{2} x\right).$

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

D. $\sin 2 x \cdot \cos \left(\sin x\right).$

A. $-\sin (2 \sin 2 x) \cdot \cos 2 x.$

B. $-\sin (2 \sin 2 x) \cdot \cos 2 x+\pi$

C. $\sin (2 \sin 2 x) \cdot \cos 2 x-1$

D. $-\sin (2 \sin 2 x) \cdot \cos 2 x-1$