Đề thi online - Đạo hàm hàm số hợp - Có lời giải c...

A 0

B 2

C 1

D Không tồn tại

A  \(y'=5{{x}^{2}}{{\left( 1-{{x}^{3}} \right)}^{4}}\)                                            

B  \(y'=-15{{x}^{2}}{{\left( 1-{{x}^{3}} \right)}^{4}}\)                 

C  \(y'=-3{{x}^{2}}{{\left( 1-{{x}^{3}} \right)}^{4}}\)                               

D  \(y'=-5{{x}^{2}}{{\left( 1-{{x}^{3}} \right)}^{4}}\)

A  \(-32\)                        

B  30                                          

C  \(-64\)                                    

D  12

A  \(y'=2\cos \sqrt{x}\)                          

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

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

D  \(y'=\frac{1}{\sqrt{x}\cos \sqrt{x}}\)

A  4                                            

B  \(\sqrt{3}\)                                         

C  \(-\sqrt{3}\)                                       

D  3

A  \(y'\left( \frac{\pi }{3} \right)=-1\)

B  \(y'\left( \frac{\pi }{3} \right)=\frac{1}{2}\)

C  \(y'\left( \frac{\pi }{3} \right)=-\frac{1}{2}\)                      

D  \(y'\left( \frac{\pi }{3} \right)=1\)

A  \(a=-4\)

B  \(a=-1\)                                  

C a = 2                           

D  \(a=-3\)

A  \(\left[ \frac{1}{\sqrt{3}};+\infty  \right)\)                           

B  \(\left( \frac{1}{\sqrt{3}};+\infty  \right)\)                           

C  \(\left( -\infty ;\frac{1}{\sqrt{3}} \right)\)                            

D  \(\left[ \frac{2}{\sqrt{3}};+\infty  \right)\)

A  \(\frac{-1}{{{\sin }^{2}}x\sqrt{\cot x}}\)               

B  \(\frac{-1}{2{{\sin }^{2}}x\sqrt{\cot x}}\)             

C  \(\frac{1}{2\sqrt{\cot x}}\)                          

D  \(\frac{-2\sin x}{2\sqrt{\cot x}}\)

A \(-\sin \left( 2{{\sin }^{3}}x \right){{\sin }^{2}}x\cos x\)              

B

 \(-6\sin \left( 2{{\sin }^{3}}x \right){{\sin }^{2}}x\cos x\)

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

D  \(-3\sin \left( 2{{\sin }^{3}}x \right){{\sin }^{2}}x\cos x\)

A  \(x+\frac{1}{2}\cos 2x\)                   

B  \(x-\frac{1}{2}\cos 2x\)                    

C  \(x-\sin 2x\)                            

D  \(x+\sin 2x\)

A  \(y'\left( 0 \right)=\frac{1}{2}\)                                

B  \(y'\left( 0 \right)=\frac{1}{3}\)                                

C  \(y'\left( 0 \right)=1\) 

D  \(y'\left( 0 \right)=2\)

A  \(f\left( \frac{\pi }{2} \right)=-1\)     

B  \(f'\left( x \right)=\frac{-2\sin 2x}{3\sqrt[3]{{{\cos }^{2}}2x}}\)              

C  \(f'\left( \frac{\pi }{2} \right)=1\)                             

D  \(3{{f}^{2}}\left( x \right)f'\left( x \right)+2\sin 2x=0\)

A  \({{\cot }^{3}}x-1\)                        

B  \(3{{\cot }^{4}}x-1\)                                   

C  \({{\cot }^{4}}x-1\)                        

D  \({{\cot }^{4}}x\)

A \(-2\cot \left( \cos x \right)\frac{1}{{{\sin }^{2}}\left( \cos x \right)}+\frac{\cos x}{2\sqrt{\sin x-\frac{\pi }{2}}}\)                     

B  \(2\cot \left( \cos x \right)\frac{1}{{{\sin }^{2}}\left( \cos x \right)}\sin x+\frac{\cos x}{2\sqrt{\sin x-\frac{\pi }{2}}}\)

C  \(-2\cot \left( \cos x \right)\frac{1}{{{\sin }^{2}}\left( \cos x \right)}+\frac{\cos x}{\sqrt{\sin x-\frac{\pi }{2}}}\)                     

D  \(2\cot \left( \cos x \right)\frac{1}{{{\sin }^{2}}\left( \cos x \right)}\sin x+\frac{\cos x}{\sqrt{\sin x-\frac{\pi }{2}}}\)

A  \(\left( 0;2 \right)\)                             

B  \(\left( -1;5 \right)\)                            

C  \(\left( -3;2 \right)\)                           

D  \(\left( 4;7 \right)\)

A  \(f'\left( 0 \right)=0\)                          

B \(f'\left( 0 \right)=1\)                          

C

 \(f'\left( 0 \right)=-2\)                        

D \(f'\left( 0 \right)=3\)

A  1 điểm                        

B  2 điểm                       

C  4 điểm                        

D  6 điểm.  

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

B  \(\frac{-1}{4}\)                                             

C  \(\frac{1}{8}\)                                              

D  \(\frac{-1}{8}\)

A  6                                            

B 2sin2x                        

C  0                                            

D  2cos2x