Trắc nghiệm Quy tắc tính đạo hàm Toán Lớp 11

A. $y^{\prime}(1)=-1 .$

B. $y^{\prime}(1)=0.$

C. $y^{\prime}(1)=-2 .$

D. $y^{\prime}(1)=-3 .$

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

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

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

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

A. $y^{\prime}=20 x-13 \text {. }$

B. $y^{\prime}=15 x-13 \text {. }$

C. $y^{\prime}=-2 x-13 \text {. }$

D. $y^{\prime}=x^2+20 x-13 \text {. }$

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

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

C. $\frac{3\left(x^{2}+10 x-2\right)}{(x+5)^{2}} \text {. }$

D. $\frac{2\left(x^{2}+10 x-2\right)}{(x+5)^{2}} \text {. }$

A. $\frac{x^{4}+5 x^{2}-4 x+12}{\left(x^{3}+4 x+2\right)^{2}}$

B. $\frac{x^{4}-4 x+12}{\left(x^{3}+4 x+2\right)^{2}}$

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

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

A. $4 x^{3}+20 x \text {. }$

B. $8 x^{3}+20 x \text {. }$

C. $21x^{3}+20 x \text {. }$

D. $-2 x^{3}+20 x \text {. }$

A. $S=\left(-\infty ;-\frac{1}{3}\right] \cup[2 ;+\infty) \text {. }$

B. $S=\left(-\infty ;-\frac{2}{3}\right) \cup[2 ;+\infty) \text {. }$

C. $S=\left(-\infty ;1\right] \cup[2 ;+\infty) \text {. }$

D. $S=\left(-\infty ;-\frac{2}{3}\right] \cup[2 ;+\infty) \text {. }$

A. x=1

B. x=2

C. x=3

D. Vô nghiệm.

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

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

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

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

A. 1

B. 0

C. 2014

D. -2

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

B. $\frac{1}{2 \sqrt{3 x+1}}+\frac{10 x}{\left(x^{2}+2\right)^{2}}$

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

D. $\frac{1}{3 \sqrt{3 x+1}}+\frac{10 x}{\left(x^{2}+2\right)^{2}}$

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

B. $\frac{2 x^{2}+4 x+4}{\sqrt{x^{2}+4}}$

C. $\frac{ x^{2}+4 x-1}{\sqrt{x^{2}+4}}$

D. $\frac{x^{2}+4 x+4}{\sqrt{x^{2}+4}}$

A. $y' = {2x^3} + 9{x^2} + \frac{5}{2}x$

B. $y' = {x^3} + 9{x^2} + \frac{5}{2}x$

C. $y' = {x^3} + 9{x^2} +5x$

D. $y' = {2x^3} + 9{x^2} +5x$

A. $\frac{{15{x^2} - 6{x}}}{{2\sqrt {5{x^3} - 3{x^2} + 1} }}$

B. $-\frac{{3{x^2} - 6{x}}}{{2\sqrt {5{x^3} - 3{x^2} + 1} }}$

C. $\frac{{15{x^2} - 6{x}}}{{\sqrt {5{x^3} - 3{x^2} + 1} }}$

D. $\frac{{5{x^2} - 6{x}}}{{2\sqrt {5{x^3} - 3{x^2} + 1} }}$

A. $y^{\prime}=12 x^{2}-3+\frac{2}{x^{2}}+\frac{1}{2 \sqrt{x}}$

B. $y^{\prime}=12 x^{2}+3+\frac{2}{x^{2}}+\frac{1}{2 \sqrt{x}}$

C. $y^{\prime}=12 x^{2}+3-\frac{2}{x^{2}}-\frac{1}{2 \sqrt{x}}$

D. $y^{\prime}=12 x^{2}+3-\frac{2}{x^{2}}+\frac{1}{2 \sqrt{x}}$

A. $y^{\prime}=\frac{2}{(3-x)^{2}}$

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

C. $y^{\prime}=\frac{7}{(3-x)^{2}}$

D. $y^{\prime}=-\frac{7}{(3-x)^{2}}$

A. $y^{\prime}=-12 x^{3}-9 x^{2}+10 x+5$

B. $y^{\prime}=21 x^{3}-9 x^{2}+10 x+5$

C. $y^{\prime}=-9 x^{3}-9 x^{2}+10 x+5$

D. $y^{\prime}=-15 x^{3}-9 x^{2}+10 x+5$

A. $y=-6 x+1$

B. $y=-3 x+1$

C. $y=-5 x+1$

D. $y=-2x-1$

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

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

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

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

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

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

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

D. $-\frac{2(\cos2 x-\sin x)}{\sin 2 x+1}$

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

B. $\frac{2}{1+\sin 2 x}$

C. $\frac{1}{1+\sin 2 x}$

D. $-\frac{1}{1+\sin 2 x}$

A. $-\frac{1}{1-\sin 2 x}$

B. $\frac{1}{1-\sin 2 x}$

C. $x-\frac{1}{1-\sin 2 x}$

D. $x+\frac{1}{1-\sin 2 x}$

A. $y^{\prime}=\frac{4(\sqrt{4 \cot x-\sin x}+\sqrt{x})-(4 x-2)\left[\frac{-4\left(1+\cot ^{2} x\right)-\cos x}{2 \sqrt{4 \cot x-\sin x}}+\frac{1}{2 \sqrt{x}}\right]}{(\sqrt{4 \cot x-\sin x}+\sqrt{x})^{2}}$

B. $y^{\prime}=\frac{4(\sqrt{4 \cot x-\sin x}+\sqrt{x})+(4 x-2)\left[\frac{-4\left(1+\cot ^{2} x\right)-\cos x}{2 \sqrt{4 \cot x-\sin x}}+\frac{1}{2 \sqrt{x}}\right]}{(\sqrt{4 \cot x-\sin x}+\sqrt{x})^{2}}$

C. $y^{\prime}=\frac{4(\sqrt{4 \cot x-\sin x}-1)}{(\sqrt{4 \cot x-\sin x}+\sqrt{x})^{2}}$

D. $y^{\prime}=\frac{4(\sqrt{4 \cot x-\sin x}+x)}{(\sqrt{4 \cot x-\sin x}+\sqrt{x})^{2}}$

A. $\frac{- \sin 6 x}{\cos ^{2} 6 x}$

B. $\frac{ \sin 6 x}{\cos ^{2} 6 x}$

C. $\frac{6 \sin 6 x}{\cos ^{2} 6 x}$

D. $\frac{ \sin 3 x}{\cos ^{2} 6 x}$

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

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

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

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

A. $\frac{\left(2x-3\right) \sin 2 x}{(\sqrt{\cos 2 x}-2)^{2} \sqrt{\cos 2 x}}-\frac{12 \sin 3 x \cdot \cos ^{3} 3 x}{\sqrt{\cos 2 x}-2}$

B. $\frac{ \sin 2 x}{(\sqrt{\cos 2 x}-2)^{2} \sqrt{\cos 2 x}}-\frac{12 \sin 3 x \cdot \cos ^{3} 3 x}{\sqrt{\cos 2 x}-2}$

C. $\frac{ \sin 2 x}{(\sqrt{\cos 2 x}-2)^{2} \sqrt{\cos 2 x}}+\frac{12 \sin 3 x \cdot \cos ^{3} 3 x}{\sqrt{\cos 2 x}-2}$

D. $\frac{\left(\cos ^{4} 3 x-1\right) \sin 2 x}{(\sqrt{\cos 2 x}-2)^{2} \sqrt{\cos 2 x}}-\frac{12 \sin 3 x \cdot \cos ^{3} 3 x}{\sqrt{\cos 2 x}-2}$

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

A. $\frac{-x-7- \sqrt{x+3}}{2 \sqrt{x+3}(x-1)^{2}} \text {. }$

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

C. $\frac{-x-7-2 \sqrt{x+3}}{2 \sqrt{x+3}(x-1)^{2}} \text {. }$

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

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

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

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

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

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

B. $-(1-\sqrt{1-2 x})^{2} \cdot \frac{1}{\sqrt{1-2 x}} \text {. }$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A. $\frac{-2}{x^{2} \sqrt{4+x^{2}}}$

B. $\frac{-4}{x^{2} \sqrt{4+x^{2}}}+1$

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

D. $\frac{-4}{x^{2} \sqrt{4+x^{2}}}$

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

B. $\frac{-5 x+8}{\left(x^{2}-x+3\right) \sqrt{x^{2}-x+3}} \text {. }$

C. $\frac{-5 x+8}{2\left(x^{2}-x+3\right) \sqrt{x^{2}-x+3}} \text {. }$

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

A. $\frac{16}{\left(16-x^{2}\right) \sqrt{16-x^{2}}} \text {. }$

B. $\frac{-1}{\left(16-x^{2}\right) \sqrt{16-x^{2}}} \text {. }$

C. $-\frac{3}{\left(16-x^{2}\right) \sqrt{16-x^{2}}} \text {. }$

D. $\frac{x+1}{\left(16-x^{2}\right) \sqrt{16-x^{2}}} \text {. }$

A. $\frac{-x}{2(x+100)^{2} \sqrt{x}} .$

B. $\frac{100-x}{2(x+100)^{2} \sqrt{x}} .$

C. $\frac{50}{(x+100)^{2} \sqrt{x}} .$

D. $\frac{1}{2(x+100)^{2} \sqrt{x}} .$

A. $-\frac{1-2 x^{2}}{\sqrt{1-x^{2}}} \text {. }$

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

C. $-\frac{1}{\sqrt{1-x^{2}}} \text {. }$

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

A. $\frac{9 x+1}{2 \sqrt{3 x+2}} \text {. }$

B. $-\frac{9 x+1}{2 \sqrt{3 x+2}} \text {. }$

C. $\frac{ x-1}{2 \sqrt{3 x+2}} \text {. }$

D. $\frac{2 x+1}{2 \sqrt{3 x+2}} \text {. }$

A. $2 x+\frac{3}{2} \sqrt{x} \text {. }$

B. $2 x-\frac{3}{2} \sqrt{x} \text {. }$

C. $2 x+\frac{3}{2} \sqrt{x}-2 \text {. }$

D. $2 x+\frac{3}{2} \sqrt{x}+1 \text {. }$

A. $\frac{1}{2} x \sqrt{x} \text {. }$

B. $\frac{5}{2} x \sqrt{x} \text {. }$

C. $-\frac{5}{2} x \sqrt{x} \text {. }$

D. $-\frac{1}{2} x \sqrt{x} \text {. }$

A. $\frac{(x-2) \sqrt{4 x-x^{2}}+2 x-4}{2 \sqrt{4 x-x^{2}}} \text {. }$

B. $\frac{(3x-2) \sqrt{4 x-x^{2}}+2 x-4}{2 \sqrt{4 x-x^{2}}} \text {. }$

C. $\frac{(x-2) \sqrt{4 x-x^{2}}+ x-2}{2 \sqrt{4 x-x^{2}}} \text {. }$

D. $-\frac{(x-2) \sqrt{4 x-x^{2}}+2 x-4}{2 \sqrt{4 x-x^{2}}} \text {. }$

A. $\frac{7 x-5}{2 \sqrt{2 x^{2}-5 x+2}}$

B. $\frac{4 x-5}{2 \sqrt{2 x^{2}-5 x+2}}+1$

C. $\frac{4 x-5}{2 \sqrt{2 x^{2}-5 x+2}}$

D. $\frac{ x-5}{2 \sqrt{2 x^{2}-5 x+2}}$

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

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

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

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

A. $\frac{2}{x^{2}}-\frac{2}{\sqrt{x}}-2 x^{3}$

B. $-\frac{1}{x^{2}}+\frac{1}{\sqrt{x}}-2 x^{3}$

C. $-\frac{2}{x^{2}}+\frac{2}{\sqrt{x}}-2 x^{3}$

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

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

B. $\frac{33\left(1-x^{2}\right)}{\left(x^{3}-3 x\right)^{12}}-\frac{1}{x^{2}}$

C. $\frac{3\left(1-x^{2}\right)}{\left(x^{3}-3 x\right)^{12}}+\frac{1}{x^{2}}$

D. $\frac{33\left(1-x^{2}\right)}{\left(x^{3}-3 x\right)^{12}}+\frac{1}{x^{2}}$

A. $\frac{6 x(2-x)}{\left(x^{3}-3 x^{2}+1\right)^{2}}$

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

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

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

A. $-\frac{1}{(3 x+5)^{3}}$

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

C. $-\frac{18}{(3 x+5)^{3}}$

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

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

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

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

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

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

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

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

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