Tính đạo hàm cấp n của hàm số \(y = \sqrt {2x + 1} \)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\({\rm{d}}y = 2\left( {x - 1} \right){\rm{d}}x\)

\({\rm{d}}y = {\left( {x - 1} \right)^2}{\rm{d}}x\)

\({\rm{d}}y = 2\left( {x - 1} \right)\)

\({\rm{d}}y = 2\left( {x - 1} \right){\rm{d}}x\)

\(dy = (3{x^2} - 4x)dx\)

\(dy = (3{x^2} + x)dx\)

\(dy = (3{x^2} + 2x)dx\)

\(dy = (3{x^2} + 4x)dx\)

\(dy = \frac{3}{{\sqrt {3x + 2} }}dx\)

\(dy = \frac{1}{{2\sqrt {3x + 2} }}dx\)

\(dy = \frac{1}{{\sqrt {3x + 2} }}dx\)

\(dy = \frac{3}{{2\sqrt {3x + 2} }}dx\)

\(dy = (1 + {\tan ^2}2x)dx\)

\(dy = (1 - {\tan ^2}2x)dx\)

\(dy = 2(1 - {\tan ^2}2x)dx\)

\(dy = 2(1 + {\tan ^2}2x)dx\)