Trắc nghiệm Hàm số mũ. Hàm số Logarit có đáp án (Thông hiểu)

A. Hàm số $y=5^{-x}$ đồng biến trên R

B. Hàm số $y={\left(\frac{\pi }{4}\right)}^{-x}$ nghịch biến trên R

C. Hàm số $y={\left(\frac{\pi }{5}\right)}^{-x}$ đồng biến trên R

D. Hàm số $y=a^{-x}\left(0<a\ne 1\right)$ luôn nghịch biến trên R

A. $y={\left(\frac{1}{3}\right)}^x$

B. $y=2^x$

C. $y=3x^3$

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

A. $y={\left(\sqrt{3}\right)}^x$

B. $y={\left(\frac{1}{2}\right)}^x$

C. $y=2^x+\frac{5}{2}$

D. $y={\left(\frac{1}{3}\right)}^x$

A. $D=\left(2;3\right)$

B. $D=(-\infty ;2]\cup [3;+\infty )$

C. $D=\left(1;6\right)$

D. $D=(2;3)$

A. $f\text{'}\left(1\right)=\pi$

B. $f\text{'}\left(1\right)={\pi }^2+\mathrm{ln\pi }$

C. $f\text{'}\left(1\right)={\pi }^2+\mathrm{\pi ln\pi }$

D. $f\text{'}\left(1\right)=1$

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

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

C. $\frac{2^{\ln x+x^2}}{\ln 2}$

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

A. $y\text{'}=\frac{e^{\sqrt{2x}}}{2\sqrt{2x}}$

B. $y\text{'}=\frac{e^{\sqrt{x}}}{\sqrt{2x}}$

C. $y\text{'}=\frac{e^{\sqrt{2x}}}{\sqrt{2x}}$

D. $y\text{'}=\sqrt{2x}.e^{\sqrt{2x}}$

A. $y\text{'}=x.x^{x-1}$

B. $y\text{'}=\left(\ln x+1\right)x^x$

C. $y\text{'}=x^x\ln x$

D. $y\text{'}=\frac{x^x}{\ln x}$

A. $y\text{'}=y\ln 3-{\ln }^{2}3$

B. $y\text{'}.\ln 3=y+\ln 3$

C. $y\text{'}=y-{\ln }^{2}3$

D. $y\text{'}=y-\ln 3$

A. $\left(3;+\infty \right)$

B. $\left(-\infty ;3\right)$

C. (2;3)

D. $\left(\infty ;1\right)$

A. $y\text{'}=\frac{2}{2x+1}$

B. $y\text{'}=\frac{1}{2x+1}$

C. $y\text{'}=\frac{2}{(2x+1)\ln 2}$

D. $y\text{'}=\frac{1}{(2x+1)\ln 2}$

A. $\left(\ln 4x\right)\text{'}=\frac{1}{x};\left(x>0\right)$

B. $\left(\ln x\right)\text{'}=\frac{1}{x\ln a};\left(x>0\right)$

C. $\left({\log }_{a}x\right)\text{'}=\frac{1}{x};\left(x>0\right)$

D. $\left({\log }_{a}x\right)\text{'}=\frac{1}{\ln a};\left(x>0\right)$

A. (1;0)

B. (a;1)

C. $\left(a^2;a\right)$

D. $\left(a^2;2\right)$

A. ${\log }_{b}a+{\log }_{a}b<0$

B. ${\log }_{b}a>1$

C. ${\log }_{a}b>0$

D. ${\log }_{b}a+{\log }_{a}b\ge 2$

A. $y\text{'}=\frac{1}{\left(5x+1\right)\ln 2}$

B. $y\text{'}=\frac{5}{\left(5x+1\right)\ln 2}$

C. $y\text{'}=\frac{1}{(5x+1)\ln 2}$

D. $y\text{'}=\frac{5}{(5x+1)\ln 2}$

A. $g\text{'}\left(x\right)=\frac{1}{x}$

B. $g\text{'}\left(x\right)=\frac{1}{x\ln 3}$

C. $g\text{'}\left(x\right)=\frac{\ln 3}{x}$

D. $g\text{'}\left(x\right)=\frac{x}{\ln 3}$

A. y=ln|x|

B. y=|lnx|

C. y=|ln(x+1)|

D. y=ln|x+1|

A. a<b<c

B. b<c<a

C. a<c<b

D. c<a<b

A. $y={2017}^x$

B. $y={\log }_{\frac{1}{2}}x$

C. $y={\log }_{\sqrt{2}}\left(x^2+1\right)$

D. $y={\left(\frac{\pi }{4}\right)}^x$

A. 1

B. 2

C. 3

D. 0