Trắc nghiệm Định nghĩa và ý nghĩa của đạo hàm Toán Lớp 11

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

B. \(y^{\prime}=\frac{3 x^{2}-4 x}{\sqrt{x^{2}-2 x}}\)

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

D. \(y^{\prime}=\frac{2 x^{2}-2 x-1}{\sqrt{x^{2}-2 x}}\)

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

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

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

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

A. \(\left[-\frac{2}{9} ; 0\right]\)

B. \(\left[-\frac{9}{2} ; 0\right]\)

C. \(\left(-\infty ;-\frac{9}{2}\right] \cup[0 ;+\infty)\)

D. \(\left(-\infty ;-\frac{2}{9}\right] \cup[0 ;+\infty)\)

A. \(y^{\prime}=\frac{2 x-2}{\left(x^{2}-2 x+5\right)^{2}}\)

B. \(y^{\prime}=\frac{-2 x+2}{\left(x^{2}-2 x+5\right)^{2}}\)

C. \(y^{\prime}=(2 x-2)\left(x^{2}-2 x+5\right)\)

D. \(y^{\prime}=\frac{1}{2 x-2}\)

A. \(4(7 x-5)^{3}\)

B. \(-28(7 x-5)^{3}\)

C. \(28(7 x-5)^{3}\)

D. \(28 x\)

A. \(y^{\prime}=10 x^{9}-28 x^{6}+16 x^{3}\)

B. \(y^{\prime}=10 x^{9}-14 x^{6}+16 x^{3}\)

C. \(y^{\prime}=10 x^{9}+16 x^{3}\)

D. \(y^{\prime}=7 x^{6}-6 x^{3}+16 x\)

A. \(y^{\prime}=\frac{5}{(2 x-1)^{2}} \cdot \sqrt{\frac{x+2}{2 x-1}}\)

B. \(y^{\prime}=\frac{1}{2} \cdot \frac{5}{(2 x-1)^{2}} \cdot \sqrt{\frac{x+2}{2 x-1}}\)

C. \(y^{\prime}=\frac{1}{2} \cdot \sqrt{\frac{x+2}{2 x-1}}\)

D. \(y^{\prime}=\frac{1}{2} \cdot \frac{5}{(x+2)^{2}} \cdot \sqrt{\frac{x+2}{2 x-1}}\)

A. \(f^{\prime}(2)=\frac{2}{\sqrt{3}}\)

B. \(f^{\prime}(2)=\frac{-2}{\sqrt{3}}\)

C. \(f^{\prime}(2)=\frac{-2}{\sqrt{-3}}\)

D. Không tồn tại.

A. \(\frac{1}{2}\)

B. \(-\frac{1}{2}\)

C. 2

D. Không tồn tại.

A. \(-14 x^{6}+2 \sqrt{x}\)

B. \(-14 x^{6}+\frac{2}{\sqrt{x}}\)

C. \(-14 x^{6}+\frac{1}{2 \sqrt{x}}\)

D. \(-14 x^{6}+\frac{1}{\sqrt{x}}\)

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

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

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

D. \(\frac{3}{x^{4}}-\frac{1}{x^{3}}\)

A. 4

B. 8

C. -4

D. 24

A. \(\frac{1}{{2}}\)

B. \(\frac{1}{\sqrt{2}}\)

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

D. \(-\frac{1}{{2}}\)

A. \(y=\frac{x^{3}-1}{x}\)

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

C. \(y=\frac{x^{3}+5 x-1}{x}\)

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

A. \(y^{\prime}=4 x^{3}-6 x^{2}+1\)

B. \(y^{\prime}=4 x^{3}-6 x^{2}+x\)

C. \(y^{\prime}=4 x^{3}-3 x^{2}+x\)

D. \(y^{\prime}=4 x^{3}-3 x^{2}+1\)

A. \(\mathbb{R} \backslash\{1\}\)

B. \(\varnothing\)

C. \((1 ;+\infty)\)

D. \(\mathbb{R}\)

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

B. \(\frac{x^{2}+6 x+7}{(x+2)^{2}}\)

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

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

A. \(\frac{1}{2}\)

B. 1

C. 0

D. Không tồn tại.

A. 1

B. 3

C. \(\emptyset\)

D. \(\mathbb{R}\)

A. \(\frac{1}{6}\)

B. \(\frac{1}{12}\)

C. \(-\frac{1}{6}\)

D. \(-\frac{1}{12}\)

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

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

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

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

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

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

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

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

A. -19

B. 7

C. 19

D. -7

A. \(\lim\limits _{\Delta x \rightarrow 0} \frac{f(x+\Delta x)-f\left(x_{0}\right)}{\Delta x}\)

B. \(\lim\limits _{x \rightarrow 0} \frac{f(x)-f\left(x_{0}\right)}{x-x_{0}}\)

C. \(\lim\limits _{x \rightarrow x_{0}} \frac{f(x)-f\left(x_{0}\right)}{x-x_{0}}\)

D. \(\lim\limits _{\Delta x \rightarrow 0} \frac{f\left(x_{0}+\Delta x\right)-f(x)}{\Delta x}\)

A. Chỉ có (1) đúng.

B. Chỉ có (2) đúng

C. Cả hai đều đúng.

D. Cả hai đều sai  

A. \(\lim \limits_{\Delta x \rightarrow 0}\left((\Delta x)^{2}+2 x \Delta x-\Delta x\right)\)

B. \(\lim\limits _{\Delta x \rightarrow 0}(\Delta x+2 x-1)\)

C. \(\lim\limits _{\Delta x \rightarrow 0}(\Delta x+2 x+1)\)

D. \(\lim \limits_{\Delta x \rightarrow 0}\left((\Delta x)^{2}+2 x \Delta x+\Delta x\right)\)

A. \(4 x+2 \Delta x+2\)

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

C. \(4 x+2 \Delta x-2\)

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

A.  Chỉ có (2) đúng.

B. Chỉ có (1) đúng.

C. Cả hai đều đúng

D. Cả hai đều sai. 

A. Có hai câu đúng và một câu sai.

B. Có một câu đúng và hai câu sai.

C. Cả ba đều đúng.

D. Cả ba đều sai.

A. \(f^{\prime}\left(x_{0}\right)=\lim\limits _{x \rightarrow x_{0}} \frac{f(x)-f\left(x_{0}\right)}{x-x_{0}}\)

B. \(f^{\prime}\left(x_{0}\right)=\lim\limits _{\Delta x \rightarrow 0} \frac{f\left(x_{0}+\Delta x\right)-f\left(x_{0}\right)}{\Delta x}\)

C. \(f^{\prime}\left(x_{0}\right)=\lim\limits _{h \rightarrow 0} \frac{f\left(x_{0}+h\right)-f\left(x_{0}\right)}{h}\)

D. \(f^{\prime}\left(x_{0}\right)=\lim \limits_{x \rightarrow x_{0}} \frac{f\left(x+x_{0}\right)-f\left(x_{0}\right)}{x-x_{0}}\)

A. \(\Delta x(\Delta x+2 x-4)\)

B. \(2 x+\Delta x\)

C. \(\Delta x \cdot(2 x-4 \Delta x)\)

D. \(2 x-4 \Delta x\)

A. 3

B. 6

C. 1

D. -6

A. \(\frac{1}{4}\)

B. \(\frac{1}{16}\)

C. \(\frac{1}{32}\)

D. Không tồn tại

A. \(\begin{array}{l} y^{\prime}=12 \sin ^{2} 2 x \cos 2 x+6 \tan 3 x+2 \tan ^{2} 3 x+\cos 4 x-4 x \sin 4 x \end{array}\)

B. \(y^{\prime}=12 \sin ^{2} 2 x \cos 2 x+6 \tan 3 x+\tan ^{2} 3 x+\cos 4 x-x \sin 4 x \)

C. \(y^{\prime}=12 \sin ^{2} 2 x \cos 2 x+\tan 3 x+\tan ^{2} 3 x+\cos 4 x-4 x \sin 4 x \)

D. \(y^{\prime}=12 \sin ^{2} 2 x \cos 2 x+6 \tan 3 x(1+\tan ^{2} 3 x)+\cos 4 x-4 x \sin 4 x\)

A. \(y^{\prime}=\left(x+\frac{2}{3 x^{2}}\right)\left(1-\frac{4}{3 x^{3}}\right)\)

B. \(y^{\prime}=2\left(x+\frac{2}{3 x^{2}}\right)\left(1+\frac{4}{3 x^{3}}\right)\)

C. \(y^{\prime}=\left(x+\frac{2}{3 x^{2}}\right)\left(1+\frac{4}{3 x^{3}}\right)\)

D. \(y^{\prime}=2\left(x+\frac{2}{3 x^{2}}\right)\left(1-\frac{4}{3 x^{3}}\right)\)

A. \(y^{\prime}=x^{4}-3 x^{2}-2\)

B. \(y^{\prime}=15 x^{4}-3 x^{2}-2\)

C. \(y^{\prime}=15 x^{4}-3 x^{2}\)

D. \(y^{\prime}=5 x^{4}-3 x^{2}-2\)

A. \(y^{\prime}=\left(x^{3}+2 x\right)^{2}\left(3 x^{2}+2\right)\)

B. \(y^{\prime}=2\left(x^{3}+2 x\right)^{2}\left(3 x^{2}+2\right)\)

C. \(y^{\prime}=3\left(x^{3}+2 x\right)^{2}+\left(3 x^{2}+2\right)\)

D. \(y^{\prime}=3\left(x^{3}+2 x\right)^{2}\left(3 x^{2}+2\right)\)

A. \(y^{\prime}=\cot ^{3} x-1\)

B. \(y^{\prime}=3 \cot ^{4} x-1\)

C. \(y^{\prime}=\cot ^{4} x-1\)

D. \(y^{\prime}=\cot ^{4} x\)

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

B. \(y^{\prime}=\frac{\sin x-x \cos x}{\sin x}\)

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

D. \(y^{\prime}=\frac{\sin x- \cos x}{\sin ^{2} x}\)

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

B. \(y^{\prime}=-3 \sin \left(2 \sin ^{3} x\right) \sin ^{2} x \cos x\)

C. \(y^{\prime}=-7 \sin \left(2 \sin ^{3} x\right) \sin ^{2} x \cos x\)

D. \(y^{\prime}=3 \sin \left(2 \sin ^{3} x\right) \sin ^{2} x \cos x\)

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

B. \(y^{\prime}=4 \cos \left(x^{2}+2\right)\)

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

D. \(y^{\prime}=4 x \cos \left(x^{2}+2\right)\)

A. \(y^{\prime}=\frac{3 x^{2}-8 \cos ^{3}\left(2 x-\frac{\pi}{4}\right) \sin \left(2 x-\frac{\pi}{4}\right)}{3 \sqrt[3]{\left(x^{3}+\cos ^{4}\left(2 x-\frac{\pi}{3}\right))^{2}\right.}}\)

B. \(y^{\prime}=\frac{6 x^{2}-8 \cos ^{3}\left(2 x-\frac{\pi}{4}\right) \sin \left(2 x-\frac{\pi}{4}\right)}{\sqrt{\left(x^{3}+\cos ^{4}\left(2 x-\frac{\pi}{3}\right))^{3}\right.}}\)

C. \(y^{\prime}=\frac{3 x^{2}-8 \cos ^{3}\left(2 x-\frac{\pi}{4}\right) \sin \left(2 x-\frac{\pi}{4}\right)}{4 \sqrt[3]{\left(x^{3}+\cos ^{4}\left(2 x-\frac{\pi}{3}\right))^{3}\right.})}\)

D. \(y^{\prime}=\frac{3 x^{2}-8 \cos ^{3}\left(2 x-\frac{\pi}{4}\right) \sin \left(2 x-\frac{\pi}{4}\right)}{3 \sqrt[3]{\left(x^{3}+\cos ^{4}\left(2 x-\frac{\pi}{3}\right))^{3}\right.})}\)

A. \(y^{\prime}=\frac{3 \tan x\left(1+\tan ^{2} x\right)-\left(1+\cot ^{2} 2 x\right)}{3 \sqrt{3 \tan ^{2} x+\cot 2 x}}\)

B. \(y^{\prime}=\frac{3 \tan x\left(1+\tan ^{2} x\right)-\left(1+\cot ^{2} 2 x\right)}{2 \sqrt{3 \tan ^{2} x+\cot 2 x}}\)

C. \(y^{\prime}=\frac{3 \tan x\left(1+\tan ^{2} x\right)-\left(1+\cot ^{2} 2 x\right)}{\sqrt{3 \tan ^{2} x+\cot 2 x}}\)

D. \(y^{\prime}=\frac{3 \tan x\left(1+\tan ^{2} x\right)+\left(1+\cot ^{2} 2 x\right)}{\sqrt{3 \tan ^{2} x+\cot 2 x}}\)

A. \(y^{\prime}=\sin 6 x\)

B. \(y^{\prime}=3 \sin 3 x\)

C. \(y^{\prime}=2 \sin 6 x\)

D. \(y^{\prime}=3 \sin 6 x\)

A. \(y^{\prime}=\frac{3- x}{2\sqrt{(1-x)^{3}}}\)

B. \(y^{\prime}=\frac{1-3 x}{3 \sqrt{(1-x)^{3}}}\)

C. \(y^{\prime}=-\frac{1}{3} \frac{1-3 x}{2 \sqrt{(1-x)^{3}}}\)

D. \(y^{\prime}=\frac{1-3 x}{2 \sqrt{(1-x)^{3}}}\)

A. \(y^{\prime}=\frac{3}{2} \frac{1}{x^{2} \sqrt{x}}\)

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

C. \(y^{\prime}=\frac{1}{x^{2} \sqrt{x}}\)

D. \(y^{\prime}=-\frac{3}{2} \frac{1}{x^{2} \sqrt{x}}\)

A. \(y^{\prime}=-\frac{a^{2}}{\sqrt{\left(a^{2}-x^{2}\right)^{3}}}\)

B. \(y^{\prime}=\frac{a^{2}}{\sqrt{\left(a^{2}+x^{2}\right)^{3}}}\)

C. \(y^{\prime}=\frac{2 a^{2}}{\sqrt{\left(a^{2}-x^{2}\right)^{3}}}\)

D. \(y^{\prime}=\frac{a^{2}}{\sqrt{\left(a^{2}-x^{2}\right)^{3}}}\)

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

B. \(y^{\prime}=2 x-\sqrt{x+1}+\frac{x}{2 \sqrt{x+1}}\)

C. \(y^{\prime}=\frac{x}{2 \sqrt{x+1}}\)

D. \(y^{\prime}=2 x+\sqrt{x+1}+\frac{x}{2 \sqrt{x+1}}\)

A. \(y^{\prime}=\frac{3 x^{2}-6 x}{\sqrt{x^{3}-3 x^{2}+2}}\)

B. \(y^{\prime}=\frac{3 x^{2}+6 x}{2 \sqrt{x^{3}-3 x^{2}+2}}\)

C. \(y^{\prime}=\frac{3 x^{2}-6 x}{2 \sqrt{x^{3}-3 x^{2}-2}}\)

D. \(y^{\prime}=\frac{3 x^{2}-6 x}{2 \sqrt{x^{3}-3 x^{2}+2}}\)

A. \(y^{\prime}=3\left(x^{2}+5 x+6\right)^{3}+2(x+3)(x+2)^{3}\)

B. \(y^{\prime}=2\left(x^{2}+5 x+6\right)^{2}+3(x+3)(x+2)^{3}\)

C. \(\begin{aligned} &y^{\prime}=3\left(x^{2}+5 x+6\right)+2(x+3)(x+2) \end{aligned}\)

D. \( y^{\prime}=3\left(x^{2}+5 x+6\right)^{2}+2(x+3)(x+2)^{3}\)