Trắc nghiệm Quy tắc tính đạo hàm Toán Lớp 11

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

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

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

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

A. $\frac{x}{\sqrt{x^{2}-2 x-8}}$

B. $\frac{x-1}{\sqrt{x^{2}-2 x-8}}$

C. $\frac{-1}{\sqrt{x^{2}-2 x-8}}$

D. $\frac{-2}{\sqrt{x^{2}-2 x-8}}$

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

B. $x^{4}-12 x^{2}+2-\frac{3}{2 \sqrt{x}} .$

C. $5 x^{4}-12 x^{2}-\frac{3}{2 \sqrt{x}} .$

D. $5 x^{4}-12 x^{2}+2-\frac{3}{2 \sqrt{x}} .$

A. $\frac{{2x + 3}}{{\sqrt {{x^2} + 6x + 7} }}$

B. $\frac{{x + 3}}{{\sqrt {{x^2} + 6x + 7} }}$

C. $\frac{{x - 3}}{{\sqrt {{x^2} + 6x + 7} }}$

D. $\frac{{x -1}}{{\sqrt {{x^2} + 6x + 7} }}$

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

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

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

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

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

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

C. $y'=8{x^3} - {x^2} + \frac{1}{{\sqrt x }}.$

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

A. $\frac{1}{x^{2}}+\frac{2}{x^{3}}-\frac{10}{(2 x-1)^{6}}$

B. $-\frac{1}{x^{2}}+\frac{2}{x^{3}}-\frac{10}{(2 x-1)^{6}}$

C. $\frac{2}{x^{3}}-\frac{10}{(2 x-1)^{6}}$

D. $\frac{1}{x^{2}}-\frac{2}{x^{3}}+\frac{10}{(2 x-1)^{6}}$

A. $1-\frac{30(2 x-3)}{\left(x^{2}-3 x\right)^{11}} .$

B. $1+\frac{30(2 x-3)}{\left(x^{2}-3 x\right)^{11}} .$

C. $1-\frac{5(2 x-3)}{\left(x^{2}-3 x\right)^{11}} .$

D. $\frac{30(2 x-3)}{\left(x^{2}-3 x\right)^{11}} .$

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

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

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

D. $\frac{1-x}{\left(x^{2}-4 x\right)^{5}}-4 x$

A. $\frac{5(2 x-1)}{\left(x^{2}-x+1\right)^{6}} .$

B. $\frac{5(1- x)}{\left(x^{2}-x+1\right)^{6}} .$

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

D. $\frac{5(1-2 x)}{\left(x^{2}-x+1\right)^{6}} .$

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

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

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

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

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

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

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

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

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

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

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

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

A. $-\frac{3}{(x-1)^{2}}-\frac{30}{(2 x-1)^{7}}$

B. $-\frac{x}{(x-1)^{2}}-\frac{30}{(2 x-1)^{7}}$

C. $-\frac{x+3}{(x-1)^{2}}-\frac{30}{(2 x-1)^{7}}$

D. $-\frac{x-3}{(x-1)^{2}}-\frac{30}{(2 x-1)^{7}}$

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

B. $\frac{-11(1-x)}{\left(x^{2}-2 x+5\right)^{3}}$

C. $\frac{9(1-x)}{\left(x^{2}-2 x+5\right)^{3}}$

D. $\frac{16(1-x)}{\left(x^{2}-2 x+5\right)^{3}}$

A. $\frac{10(3-2 x)}{\left(3 x-x^{2}\right)^{6}}-\frac{1}{x^{2}}$

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

C. $\frac{-4(3-2 x)}{\left(3 x-x^{2}\right)^{6}}-\frac{3}{x^{2}}$

D. $\frac{-4(3-2 x)}{\left(3 x-x^{2}\right)^{6}}-\frac{1}{x^{2}}$

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

B. $-\frac{x+1}{(2 x-5)^{3}} .$

C. $-\frac{x-1}{(2 x-5)^{3}} .$

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

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

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

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

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

A. $1+\frac{9}{x^{2}}- \cdot \frac{\left(4 x^{3}+18 x^{2}\right)}{\left(x^{4}+6 x^{3}-1\right)^{2}}$

B. $-\frac{9}{x^{2}}+2 \cdot \frac{\left(4 x^{3}+18 x^{2}\right)}{\left(x^{4}+6 x^{3}-1\right)^{2}}$

C. $-\frac{9}{x^{2}}+2 \cdot \frac{\left(4 x^{3}+18 x^{2}\right)}{\left(x^{4}+6 x^{3}-1\right)^{2}}$

D. $1+\frac{9}{x^{2}}+2 \cdot \frac{\left(4 x^{3}+18 x^{2}\right)}{\left(x^{4}+6 x^{3}-1\right)^{2}}$

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

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

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

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

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

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

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

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

A. $y^{\prime}=\frac{10 x+9}{\left(x^{2}+x+2\right)^{2}} \text {. }$

B. $y^{\prime}=\frac{-x+9}{\left(x^{2}+x+2\right)^{2}} \text {. }$

C. $y^{\prime}=\frac{-2 x^{2}+10 x+9}{\left(x^{2}+x+2\right)^{2}} \text {. }$

D. $y^{\prime}=\frac{- x^{2}+10 x+4}{\left(x^{2}+x+2\right)^{2}} \text {. }$

A. $\frac{2 x^{2}-10 x+1}{(2 x-5)^{2}}$

B. $\frac{10 x+1}{(2 x-5)^{2}}$

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

D. $\frac{3 x^{2}-5 x+1}{(3 x-5)^{2}}$

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

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

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

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

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

B. $\frac{3x^{2}-2 x+m-5}{(x-1)^{2}} .$

C. $\frac{x^{2}-2 x+m-5}{(x-1)^{2}} .$

D. $\frac{-2 x+m-5}{(x-1)^{2}} .$

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

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

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

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

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

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

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

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

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

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

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

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

A. $\frac{11}{(x+5)^{2}}$

B. $\frac{-11}{(x+5)^{2}}$

C. $\frac{x+11}{(x+5)^{2}}$

D. $\frac{x-11}{(x+5)^{2}}$

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

B. $\frac{5-x}{(1-3 x)^{2}} .$

C. $\frac{-5}{(1-3 x)^{2}} .$

D. $\frac{5}{(1-3 x)^{2}} .$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A. $10\left(12 x^{2}-10 x+3\right)(x+3)^{5}\left(3 x-5 x^{2}+4 x^{3}\right)^{9}+5(x+3)^{4}\left(3 x-5 x^{2}+4 x^{3}\right)^{10} .$

B. $10\left(12 x^{2}- x+5\right)(x+3)^{5}\left(3 x-5 x^{2}-4 x^{3}\right)^{9}+5(x+3)^{4}\left(3 x-5 x^{2}+4 x^{3}\right)^{10} .$

C. $10\left(12 x^{2}- x+3\right)(x+3)^{5}\left(3 x-5 x^{2}+ x^{3}\right)^{9}-5(x+3)^{4}\left(3 x-5 x^{2}+4 x^{3}\right)^{10} .$

D. $(x+3)^{5}\left(3 x-5 x^{2}+4 x^{3}\right)^{9}+5(x+3)^{4}\left(3 x-5 x^{2}+4 x^{3}\right)^{10} .$

A. $x^{7}-24 x^{5}+10 x^{4}+8 x^{3}-12 x^{2}+10 x-2 .$

B. $8 x^{7}-24 x^{5}+10 x^{4}+8 x^{3}-12 x^{2}+10 x-2 .$

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

D. $-24 x^{5}+10 x^{4}+8 x^{3}-12 x^{2}+10 x-2 .$

A. $10{\left( {{x^7} + 3{x^4} + 2} \right)^9}$

B. $10{\left( {{x^7} + 3{x^4} + 2} \right)^9} + \left( {7{x^6} + 12{x^3}} \right)$

C. $10{\left( {{x^7} + 3{x^4} + 2} \right)^{10}} \cdot \left( {8{x^6} + 12{x^3}} \right)$

D. $10{\left( {{x^7} + 3{x^4} + 2} \right)^9} \cdot \left( {7{x^6} + 12{x^3}} \right)$

A. $-60 x^{4}-60 x^{3}+120 x^{2}+60 x-12 .$

B. $24 x^{5}-60 x^{4}-60 x^{3}+120 x^{2}+60 x-12 .$

C. $-2 x^{5}-60 x^{4}-60 x^{3}+120 x^{2}+60 x-12 .$

D. $x^6-24 x^{5}-60 x^{4}-60 x^{3}+120 x^{2}+60 x-12 .$

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

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

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

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

A. $-3 x^{13}+14 x^{7}+2 x \text {. }$

B. $14 x^{13}+8 x^{7}+2 x \text {. }$

C. $14 x^{13}+16 x^{7}+2 x \text {. }$

D. $x^{13}- x^{7}+2 x \text {. }$

A. $18 x^{2}+2 x-2 .$

B. $9x^{2}+2 x-2 .$

C. $12 x^{2}+2 x-2 .$

D. $3 x^{2}+2 x-2 .$

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

B. $4x^{2}+4 .$

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

D. $16 x^{2}+4 .$

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

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

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

D. $-2 x^{3}- x^{2}+ x+3$

A. $9 x^{2}+4(m-1) x+1 .$

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

C. $9 x^{2}+4 x+1 .$

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

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

B. $-2x^{3}+x^{2}+x$

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

D. $-2x^{3}-x^{2}+x$

A. $x^{4}-8 x^{3}+x^{2}$

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

C. $m x^{4}- x^{3}+x^{2}$

D. $m x^{4}-8 x^{3}+x^{2}$

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

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

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

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

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

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

C. $\frac{1}{2}{x^4} + 4{x^3} - 3{x^2} - 3x + 4$

D. $\frac{5}{2}{x^4} + 4{x^3} - 3{x^2} - 3x + 4$

A. $y'=3 x^{2}-6 x+1$

B. $y'= x^{2}-6 x+1$

C. $y'=3 x^{3}-6 x+1$

D. $y'=-2 x^{2}-6 x+1$

A. $y'=-12 x^{3}+8 x-3 .$

B. $y'=- x^{3}+8 x$

C. $y'=-8 x^{3}+8 x-3 .$

D. $y'=- x^{3}+8 x-3 .$