Cho hàm số \[y = f\left( x \right) = - \frac{1}{x}\]. Xét hai mệnh đề:

(I): \[y\prime \prime = f\prime \prime (x) = \frac{2}{{{x^3}}}\]

(II): \[y\prime \prime \prime = f\prime \prime \prime (x) = - \frac{6}{{{x^4}}}\]

Mệnh đề nào đúng?

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

A.\[12\,m/{s^2}\]

B. \[8\,m/{s^2}\]

C. \[7\,m/{s^2}\]

D. \[6\,m/{s^2}\]

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.−cosx 

B.sinx 

C.−sinx 

D.cosx 

A.\[dy = {\left( {{x^2} + 2x} \right)^\prime }dx\]

B. \[dx = {\left( {{x^2} + 2x} \right)^\prime }dy\]

C. \[dy = \left( {{x^2} + 2x} \right)dx\]

D. \[dy = \frac{1}{{{x^2} + 2x}}dx\]

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.\[y'' = - \frac{{2\sin x}}{{{{\cos }^3}x}}\]

B. \[y'' = \frac{1}{{{{\cos }^2}x}}\]

C. \[y'' = - \frac{1}{{{{\cos }^2}x}}\]

D. \[y'' = \frac{{2\sin x}}{{{{\cos }^3}x}}\]