Производная ((x+1)/(x-1))^(1/5)*log(3,x^(2)+x+4)

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    _______                   
   / x + 1     /    2        \
5 /  ----- *log\3, x  + x + 4/
\/   x - 1                    
$$\sqrt[5]{\frac{x + 1}{x - 1}} \log{\left (3,x^{2} + x + 4 \right )}$$
Первая производная
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                                                               _______                                                    
                                                              / x + 1          /    1         x + 1   \    /    2        \
                                                           5 /  ----- *(x - 1)*|--------- - ----------|*log\3, x  + x + 4/
    _______                                                \/   x - 1          |5*(x - 1)            2|                   
   / x + 1            /  d  /  log(3) \\|                                      \            5*(x - 1) /                   
5 /  ----- *(1 + 2*x)*|-----|---------|||      2         + ---------------------------------------------------------------
\/   x - 1            \dxi_2\log(xi_2)//|xi_2=x  + x + 4                                x + 1                             
$$\frac{\sqrt[5]{\frac{x + 1}{x - 1}}}{x + 1} \left(x - 1\right) \left(\frac{1}{5 x - 5} - \frac{x + 1}{5 \left(x - 1\right)^{2}}\right) \log{\left (3,x^{2} + x + 4 \right )} + \sqrt[5]{\frac{x + 1}{x - 1}} \left(2 x + 1\right) \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=x^{2} + x + 4 }}$$
Вторая производная
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             /                                                                                    2                                                                                    2 /           2       \                                            \
             |                                          /    1 + x \                  /    1 + x \                          /    1 + x \ /  d  /  log(3) \\|                  (1 + 2*x) *|1 + ---------------|*log(3)          /    1 + x \               |
    ________ |                                          |1 - ------|*log(3)           |1 - ------| *log(3)      2*(1 + 2*x)*|1 - ------|*|-----|---------|||              2              |       /         2\|                 |1 - ------|*log(3)        |
   / 1 + x   |  /  d  /  log(3) \\|                     \    -1 + x/                  \    -1 + x/                          \    -1 + x/ \dxi_2\log(xi_2)//|xi_2=4 + x + x               \    log\4 + x + x //                 \    -1 + x/               |
5 /  ------ *|2*|-----|---------|||      2         - -------------------------- + --------------------------- + ----------------------------------------------------------- + --------------------------------------- - ----------------------------------|
\/   -1 + x  |  \dxi_2\log(xi_2)//|xi_2=x  + x + 4            2    /         2\             2    /         2\                            5*(1 + x)                                             2                                              /         2\|
             |                                       5*(1 + x) *log\4 + x + x /   25*(1 + x) *log\4 + x + x /                                                                      /         2\     2/         2\       5*(1 + x)*(-1 + x)*log\4 + x + x /|
             \                                                                                                                                                                     \4 + x + x / *log \4 + x + x /                                         /
$$\sqrt[5]{\frac{x + 1}{x - 1}} \left(\frac{\left(1 - \frac{x + 1}{x - 1}\right)^{2} \log{\left (3 \right )}}{25 \left(x + 1\right)^{2} \log{\left (x^{2} + x + 4 \right )}} + \frac{2}{5 x + 5} \left(1 - \frac{x + 1}{x - 1}\right) \left(2 x + 1\right) \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=x^{2} + x + 4 }} - \frac{\left(1 - \frac{x + 1}{x - 1}\right) \log{\left (3 \right )}}{5 \left(x + 1\right)^{2} \log{\left (x^{2} + x + 4 \right )}} - \frac{\left(1 - \frac{x + 1}{x - 1}\right) \log{\left (3 \right )}}{5 \left(x - 1\right) \left(x + 1\right) \log{\left (x^{2} + x + 4 \right )}} + \frac{\left(1 + \frac{2}{\log{\left (x^{2} + x + 4 \right )}}\right) \left(2 x + 1\right)^{2} \log{\left (3 \right )}}{\left(x^{2} + x + 4\right)^{2} \log^{2}{\left (x^{2} + x + 4 \right )}} + 2 \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=x^{2} + x + 4 }}\right)$$
Третья производная
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             /                                                                                                                                                                    2                            3                                                         2                                                           3 /           2       \                     3 /           2       \                      /           2       \                                                                                             2                                                                                                        2 /           2       \ /    1 + x \       \
             |  /    1 + x \ /  d  /  log(3) \\|                                                               /    1 + x \ /  d  /  log(3) \\|                       /    1 + x \                 /    1 + x \                   /    1 + x \               /    1 + x \            /  d  /  log(3) \\|                  2*(1 + 2*x) *|1 + ---------------|*log(3)   2*(1 + 2*x) *|1 + ---------------|*log(3)   6*(1 + 2*x)*|1 + ---------------|*log(3)               /    1 + x \ /  d  /  log(3) \\|                           /    1 + x \                           /    1 + x \                          /    1 + x \                 3*(1 + 2*x) *|1 + ---------------|*|1 - ------|*log(3)|
    ________ |6*|1 - ------|*|-----|---------|||              2                   3                3*(1 + 2*x)*|1 - ------|*|-----|---------|||              2      3*|1 - ------| *log(3)         |1 - ------| *log(3)         2*|1 - ------|*log(3)      3*|1 - ------| *(1 + 2*x)*|-----|---------|||              2                |       /         2\|                       |       /         2\|                      |       /         2\|          3*(1 + 2*x)*|1 - ------|*|-----|---------|||              2          3*|1 - ------| *log(3)                 2*|1 - ------|*log(3)                 2*|1 - ------|*log(3)                       |       /         2\| \    -1 + x/       |
   / 1 + x   |  \    -1 + x/ \dxi_2\log(xi_2)//|xi_2=4 + x + x         2*(1 + 2*x) *log(3)                     \    -1 + x/ \dxi_2\log(xi_2)//|xi_2=4 + x + x         \    -1 + x/                 \    -1 + x/                   \    -1 + x/               \    -1 + x/            \dxi_2\log(xi_2)//|xi_2=4 + x + x                 \    log\4 + x + x //                       \    log\4 + x + x //                      \    log\4 + x + x //                      \    -1 + x/ \dxi_2\log(xi_2)//|xi_2=4 + x + x             \    -1 + x/                           \    -1 + x/                          \    -1 + x/                              \    log\4 + x + x //                    |
5 /  ------ *|------------------------------------------------- - ------------------------------ - ----------------------------------------------------------- - --------------------------- + ---------------------------- + -------------------------- + ------------------------------------------------------------ - ----------------------------------------- - ----------------------------------------- + ---------------------------------------- - ----------------------------------------------------------- - ------------------------------------ + ----------------------------------- + ----------------------------------- + ------------------------------------------------------|
\/   -1 + x  |                    5*(1 + x)                                   3                                                      2                                     3    /         2\              3    /         2\            3    /         2\                                     2                                              3                                           3                                          2                                              5*(1 + x)*(-1 + x)                                 2             /         2\                     2    /         2\            2             /         2\                                2                        |
             |                                                    /         2\     4/         2\                            5*(1 + x)                            25*(1 + x) *log\4 + x + x /   125*(1 + x) *log\4 + x + x /   5*(1 + x) *log\4 + x + x /                           25*(1 + x)                                   /         2\     3/         2\              /         2\     2/         2\             /         2\     2/         2\                                                                      25*(1 + x) *(-1 + x)*log\4 + x + x /   5*(1 + x)*(-1 + x) *log\4 + x + x /   5*(1 + x) *(-1 + x)*log\4 + x + x /                    /         2\     2/         2\       |
             \                                                    \4 + x + x / *log \4 + x + x /                                                                                                                                                                                                                                \4 + x + x / *log \4 + x + x /              \4 + x + x / *log \4 + x + x /             \4 + x + x / *log \4 + x + x /                                                                                                                                                                                                5*(1 + x)*\4 + x + x / *log \4 + x + x /       /
$$\sqrt[5]{\frac{x + 1}{x - 1}} \left(\frac{\left(1 - \frac{x + 1}{x - 1}\right)^{3} \log{\left (3 \right )}}{125 \left(x + 1\right)^{3} \log{\left (x^{2} + x + 4 \right )}} + \frac{3 \left(1 - \frac{x + 1}{x - 1}\right)^{2}}{25 \left(x + 1\right)^{2}} \left(2 x + 1\right) \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=x^{2} + x + 4 }} - \frac{3 \left(1 - \frac{x + 1}{x - 1}\right)^{2} \log{\left (3 \right )}}{25 \left(x + 1\right)^{3} \log{\left (x^{2} + x + 4 \right )}} - \frac{3 \left(1 - \frac{x + 1}{x - 1}\right)^{2} \log{\left (3 \right )}}{25 \left(x - 1\right) \left(x + 1\right)^{2} \log{\left (x^{2} + x + 4 \right )}} + \frac{3 \left(1 - \frac{x + 1}{x - 1}\right) \left(1 + \frac{2}{\log{\left (x^{2} + x + 4 \right )}}\right) \left(2 x + 1\right)^{2} \log{\left (3 \right )}}{5 \left(x + 1\right) \left(x^{2} + x + 4\right)^{2} \log^{2}{\left (x^{2} + x + 4 \right )}} + \frac{6}{5 x + 5} \left(1 - \frac{x + 1}{x - 1}\right) \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=x^{2} + x + 4 }} - \frac{3}{5 \left(x + 1\right)^{2}} \left(1 - \frac{x + 1}{x - 1}\right) \left(2 x + 1\right) \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=x^{2} + x + 4 }} + \frac{2 \left(1 - \frac{x + 1}{x - 1}\right) \log{\left (3 \right )}}{5 \left(x + 1\right)^{3} \log{\left (x^{2} + x + 4 \right )}} - \frac{3}{5 \left(x - 1\right) \left(x + 1\right)} \left(1 - \frac{x + 1}{x - 1}\right) \left(2 x + 1\right) \left. \frac{d}{d \xi_{2}}\left(\frac{\log{\left (3 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=x^{2} + x + 4 }} + \frac{2 \left(1 - \frac{x + 1}{x - 1}\right) \log{\left (3 \right )}}{5 \left(x - 1\right) \left(x + 1\right)^{2} \log{\left (x^{2} + x + 4 \right )}} + \frac{2 \left(1 - \frac{x + 1}{x - 1}\right) \log{\left (3 \right )}}{5 \left(x - 1\right)^{2} \left(x + 1\right) \log{\left (x^{2} + x + 4 \right )}} - \frac{2 \left(1 + \frac{2}{\log{\left (x^{2} + x + 4 \right )}}\right) \left(2 x + 1\right)^{3} \log{\left (3 \right )}}{\left(x^{2} + x + 4\right)^{3} \log^{2}{\left (x^{2} + x + 4 \right )}} - \frac{2 \left(1 + \frac{2}{\log{\left (x^{2} + x + 4 \right )}}\right) \left(2 x + 1\right)^{3} \log{\left (3 \right )}}{\left(x^{2} + x + 4\right)^{3} \log^{3}{\left (x^{2} + x + 4 \right )}} + \frac{6 \left(1 + \frac{2}{\log{\left (x^{2} + x + 4 \right )}}\right) \left(2 x + 1\right) \log{\left (3 \right )}}{\left(x^{2} + x + 4\right)^{2} \log^{2}{\left (x^{2} + x + 4 \right )}} - \frac{2 \left(2 x + 1\right)^{3} \log{\left (3 \right )}}{\left(x^{2} + x + 4\right)^{3} \log^{4}{\left (x^{2} + x + 4 \right )}}\right)$$