Cho hàm số \(f\left( x \right) = {\sin ^3}x + {x^2}\). Giá trị \(f''\left( {\frac{\pi }{2}} \right)\) bằng

\[{y^{\left( {10} \right)}}\left( 1 \right) = 0\]

\[{y^{\left( {10} \right)}}\left( 1 \right) = 10a + b\]

\[{y^{\left( {10} \right)}}\left( 1 \right) = 5a\]

\[{y^{\left( {10} \right)}}\left( 1 \right) = 10a\]

4 và 16

5 và 17

6 và 18

7 và 19

\({y^{(n)}} = \frac{{{{(1)}^{n - 1}}.3.n!}}{{{{(x + 2)}^{n + 1}}}}\)

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

\({y^{(n)}} = \frac{{{{( - 1)}^{n - 1}}.3.n!}}{{{{(x - 2)}^{n + 1}}}}\)

\({y^{(n)}} = \frac{{{{( - 1)}^{n - 1}}.3.n!}}{{{{(x + 2)}^{n + 1}}}}\)

\({y^{(n)}} = \frac{{{{(2)}^n}.7.n!}}{{{{(x - 2)}^{n + 1}}}} - \frac{{{{(1)}^n}.5.n!}}{{{{(x - 3)}^{n + 1}}}}\)

\({y^{(n)}} = \frac{{{{( - 1)}^{n + 1}}.7.n!}}{{{{(x - 2)}^{n + 1}}}} - \frac{{{{( - 1)}^{n + 1}}.5.n!}}{{{{(x - 3)}^{n + 1}}}}\)

\({y^{(n)}} = \frac{{{{( - 1)}^n}.7.n!}}{{{{(x - 2)}^n}}} - \frac{{{{( - 1)}^n}.5.n!}}{{{{(x - 3)}^n}}}\)

\({y^{(n)}} = \frac{{{{( - 1)}^n}.7.n!}}{{{{(x - 2)}^{n + 1}}}} - \frac{{{{( - 1)}^n}.5.n!}}{{{{(x - 3)}^{n + 1}}}}\)

\({y^{(n)}} = \frac{{{{( - 1)}^{n + 1}}.3.5...(3n - 1)}}{{\sqrt {{{(2x + 1)}^{2n - 1}}} }}\)

\({y^{(n)}} = \frac{{{{( - 1)}^{n - 1}}.3.5...(2n - 1)}}{{\sqrt {{{(2x + 1)}^{2n - 1}}} }}\)

\({y^{(n)}} = \frac{{{{( - 1)}^{n + 1}}.3.5...(2n - 1)}}{{\sqrt {{{(2x + 1)}^{2n + 1}}} }}\)

\({y^{(n)}} = \frac{{{{( - 1)}^{n + 1}}.3.5...(2n - 1)}}{{\sqrt {{{(2x + 1)}^{2n - 1}}} }}\)

\({y^{(n)}} = \frac{{5.{{( - 1)}^n}.n!}}{{{{(x - 2)}^{n + 1}}}} + \frac{{3.{{( - 1)}^n}.n!}}{{{{(x - 1)}^{n + 1}}}}\)

\({y^{(n)}} = \frac{{5.{{( - 1)}^n}.n!}}{{{{(x + 2)}^{n + 1}}}} - \frac{{3.{{( - 1)}^n}.n!}}{{{{(x - 1)}^{n + 1}}}}\)

\({y^{(n)}} = \frac{{5.{{( - 1)}^n}.n!}}{{{{(x - 2)}^{n + 1}}}}:\frac{{3.{{( - 1)}^n}.n!}}{{{{(x - 1)}^{n + 1}}}}\)

\({y^{(n)}} = \frac{{5.{{( - 1)}^n}.n!}}{{{{(x - 2)}^{n + 1}}}} - \frac{{3.{{( - 1)}^n}.n!}}{{{{(x - 1)}^{n + 1}}}}\)

\[{y^{(n)}} = \frac{{{{( - 1)}^n}.3.n!}}{{{{(x + 3)}^{n + 1}}}} + \frac{{{{( - 1)}^n}.2.n!}}{{{{(x + 2)}^{n + 1}}}}\]

\[{y^{(n)}} = \frac{{{{( - 1)}^n}.3.n!}}{{{{(x + 3)}^n}}} - \frac{{{{( - 1)}^n}.2.n!}}{{{{(x + 2)}^n}}}\]

\[{y^{(n)}} = \frac{{{{( - 1)}^n}.3.n!}}{{{{(x + 3)}^{n - 1}}}} - \frac{{{{( - 1)}^n}.2.n!}}{{{{(x + 2)}^{n - 1}}}}\]

\[{y^{(n)}} = \frac{{{{( - 1)}^n}.3.n!}}{{{{(x + 3)}^{n + 1}}}} - \frac{{{{( - 1)}^n}.2.n!}}{{{{(x + 2)}^{n + 1}}}}\]

\({y^{(n)}} = {2^{n + 1}}\cos \left( {2x + n\frac{\pi }{2}} \right)\)

\({y^{(n)}} = {2^{n - 1}}\cos \left( {2x + n\frac{\pi }{2}} \right)\)

\({y^{(n)}} = {2^n}\cos \left( {2x + \frac{\pi }{2}} \right)\)

\({y^{(n)}} = {2^n}\cos \left( {2x + n\frac{\pi }{2}} \right)\)

$\sum _{n=1}^{\infty }\frac{n}{n^4+1}$

$\sum _{n=1}^{\infty }\frac{{(-1)}^n}{n^2}$

$\sum _{n=1}^{\infty }\frac{{(-1)}^n\cos \left(\mathrm{\pi n}\right)}{\sqrt{n}}$

$\sum _{n=1}^{\infty }\frac{1}{3^n}$

$A.\sum _{n=1}^{\infty }\frac{1}{n}$

$B.\sum _{n=1}^{\infty }{\left(\frac{1}{5}\right)}^n$

$C.\sum _{n=1}^{\infty }\left(\frac{1}{n^4}\right)$

$\underset{n=1}{\overset{\infty }{D.\sum }}\frac{1}{\sqrt{n}}$