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A  \(y''=0\)                      

B  \(y''=\frac{1}{{{\left( x-2 \right)}^{2}}}\)              

C \(y''=-\frac{4}{{{\left( x-2 \right)}^{3}}}\)              

D  \(y''=\frac{4}{{{\left( x-2 \right)}^{3}}}\)

A \(y'''=12x\left( {{x}^{2}}+1 \right)\)                                    

B \(y'''=24x\left( {{x}^{2}}+1 \right)\)            

C \(y'''=24x\left( 5{{x}^{2}}+3 \right)\)                                  

D  \(y'''=-12x\left( {{x}^{2}}+1 \right)\)

A  \(y''=\frac{1}{\left( 2x+5 \right)\sqrt{2x+5}}\)                                

B  \(y''=\frac{1}{\sqrt{2x+5}}\)                       

C  \(y''=-\frac{1}{\left( 2x+5 \right)\sqrt{2x+5}}\)                              

D  \(y''=-\frac{1}{\sqrt{2x+5}}\)

A  \(y''=-\frac{2\sin x}{{{\cos }^{3}}x}\)                    

B  \(y''=\frac{1}{{{\cos }^{2}}x}\)                 

C  \(y''=-\frac{1}{{{\cos }^{2}}x}\)                

D \(y''=\frac{2\sin x}{{{\cos }^{3}}x}\)

A  \(f'''\left( x \right)=80{{\left( 2x+5 \right)}^{3}}\)                          

B  \(f'''\left( x \right)=480{{\left( 2x+5 \right)}^{2}}\)

C \(f'''\left( x \right)=-480{{\left( 2x+5 \right)}^{2}}\)                                    

D  \(f'''\left( x \right)=-80{{\left( 2x+5 \right)}^{3}}\)

A  \(\left[ -1;2 \right]\)                            

B  \(\left( -\infty ;0 \right]\)                                

C  \(\left\{ -1 \right\}\)                           

D  \(\varnothing \)

A  \(y'=\sin \left( x+\frac{\pi }{2} \right)\)                                            

B \(y''=\sin \left( x+\pi  \right)\)              

C  \(y'''=\sin \left( x+\frac{3\pi }{2} \right)\)                                         

D  \({{y}^{\left( 4 \right)}}=\sin \left( 2\pi -x \right)\)

A \(x=\frac{\pi }{2}\)                

B  \(x=0\) hoặc \(x=\frac{\pi }{6}\)                   

C \(x=0\) hoặc \(x=\frac{\pi }{3}\)                    

D \(x=0\) hoặc \(x=\frac{\pi }{2}\)

A  \(4y-y''=0\)                 

B  \(4y+y''=0\)                

C  \(y=y'\tan 2x\)                        

D  \({{y}^{2}}={{\left( y' \right)}^{2}}=4\)

A  Chỉ (I)                       

B  Chỉ (II) đúng             

C  Cả hai đều đúng                    

D  Cả hai đều sai.

A 0

B 1

C -2

D 5

A  \(y''=-\frac{2{{x}^{3}}+3x}{\left( 1+{{x}^{2}} \right)\sqrt{1+{{x}^{2}}}}\)                          

B \(y''=\frac{2{{x}^{2}}+1}{\sqrt{1+{{x}^{2}}}}\)

C  \(y''=\frac{2{{x}^{3}}+3x}{\left( 1+{{x}^{2}} \right)\sqrt{1+{{x}^{2}}}}\)                           

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

A  \(\frac{1}{\cos x}\)                           

B \(-\frac{1}{\cos x}\)                          

C  \(\cot x\)                                 

D  \(\tan x\)

A  \({{f}^{\left( 10 \right)}}\left( 1 \right)=0\)             

B  \({{f}^{\left( 10 \right)}}\left( 1 \right)=10a+b\)                 

C  \({{f}^{\left( 10 \right)}}\left( 1 \right)=5a\)                       

D  \({{f}^{\left( 10 \right)}}\left( 1 \right)=10a\)

A \(-\cos x\)                                

B \(\sin x\)                                  

C  \(-\sin x\)                                

D  \(\cos x\)

A  \(12\,m/{{s}^{2}}\)                          

B  \(8\,m/{{s}^{2}}\)                            

C  \(7\,m/{{s}^{2}}\)                            

D  \(6\,m/{{s}^{2}}\)

A  \({{y}^{\left( 4 \right)}}=-2048\cos 8x+8\cos 2x\)                          

B  \({{y}^{\left( 4 \right)}}=2048\cos 8x-8\cos 2x\)

C  \({{y}^{\left( 4 \right)}}=1024\cos 16x+4\cos 4x\)                         

D  \({{y}^{\left( 4 \right)}}=2048\cos 8x-4\cos 4x\)

A  \({{y}^{3}}.y''+1=0\)                       

B  \({{y}^{2}}.y''-1=0\)                        

C  \(3{{y}^{2}}.y''+1=0\)                     

D  \(2{{y}^{3}}.y''+3=0\)

A \({{y}^{\left( n \right)}}=\dfrac{{{2}^{n}}.{{a}^{n}}.n!}{{{\left( ax+b \right)}^{n+1}}}\)                                                       

B \({{y}^{\left( n \right)}}=\dfrac{{{\left( -1 \right)}^{n}}{{a}^{n}}n!}{{{\left( x+1 \right)}^{n+1}}}\)        

C \({{y}^{\left( n \right)}}=\dfrac{{{\left( -1 \right)}^{n}}.n!}{{{\left( ax+b \right)}^{n+1}}}\)

D \({{y}^{\left( n \right)}}=\dfrac{{{\left( -1 \right)}^{n}}.{{a}^{n}}.n!}{{{\left( ax+b \right)}^{n+1}}}\)

A  \({{y}^{\left( 4 \right)}}=\frac{7.4!}{{{\left( x-3 \right)}^{5}}}-\frac{5.4!}{{{\left( x-2 \right)}^{5}}}\)                                                

B  \({{y}^{\left( 4 \right)}}=\frac{5.4!}{{{\left( x-3 \right)}^{5}}}-\frac{2.4!}{{{\left( x-2 \right)}^{5}}}\)

C  \({{y}^{\left( 4 \right)}}=\frac{5.4!}{{{\left( x-2 \right)}^{5}}}-\frac{7.4!}{{{\left( x-3 \right)}^{5}}}\)                                               

D  \({{y}^{\left( 4 \right)}}=\frac{7}{{{\left( x-3 \right)}^{4}}}-\frac{5}{{{\left( x-2 \right)}^{4}}}\)