Производная log((1/2),sqrt(2)/(3*x+1))

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Решение

Вы ввели
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   /        ___ \
   |      \/ 2  |
log|1/2, -------|
   \     3*x + 1/
$$\log{\left (\frac{1}{2},\frac{\sqrt{2}}{3 x + 1} \right )}$$
График
Первая производная
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     ___ /  d  / -log(2) \\|        ___ 
-3*\/ 2 *|-----|---------|||      \/ 2  
         \dxi_2\log(xi_2)//|xi_2=-------
                                 3*x + 1
----------------------------------------
                        2               
               (3*x + 1)                
$$- \frac{3 \sqrt{2}}{\left(3 x + 1\right)^{2}} \left. \frac{d}{d \xi_{2}}\left(- \frac{\log{\left (2 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=\frac{\sqrt{2}}{3 x + 1} }}$$
Вторая производная
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  /  /         2      \                                                 \
  |  |1 + ------------|*log(2)                                          |
  |  |       /   ___ \|              ___ /  d  / -log(2) \\|        ___ |
  |  |       | \/ 2  ||          2*\/ 2 *|-----|---------|||      \/ 2  |
  |  |    log|-------||                  \dxi_2\log(xi_2)//|xi_2=-------|
  |  \       \1 + 3*x//                                          3*x + 1|
9*|- ------------------------- + ---------------------------------------|
  |            /   ___ \                         1 + 3*x                |
  |           2| \/ 2  |                                                |
  |        log |-------|                                                |
  \            \1 + 3*x/                                                /
-------------------------------------------------------------------------
                                         2                               
                                (1 + 3*x)                                
$$\frac{1}{\left(3 x + 1\right)^{2}} \left(- \frac{9 \left(1 + \frac{2}{\log{\left (\frac{\sqrt{2}}{3 x + 1} \right )}}\right) \log{\left (2 \right )}}{\log^{2}{\left (\frac{\sqrt{2}}{3 x + 1} \right )}} + \frac{18 \sqrt{2}}{3 x + 1} \left. \frac{d}{d \xi_{2}}\left(- \frac{\log{\left (2 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=\frac{\sqrt{2}}{3 x + 1} }}\right)$$
Третья производная
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   /                  /         2      \                                                      /         2      \       \
   |                  |1 + ------------|*log(2)                                             2*|1 + ------------|*log(2)|
   |                  |       /   ___ \|              ___ /  d  / -log(2) \\|        ___      |       /   ___ \|       |
   |                  |       | \/ 2  ||          3*\/ 2 *|-----|---------|||      \/ 2       |       | \/ 2  ||       |
   |                  |    log|-------||                  \dxi_2\log(xi_2)//|xi_2=-------     |    log|-------||       |
   |      log(2)      \       \1 + 3*x//                                          3*x + 1     \       \1 + 3*x//       |
54*|- ------------- - ------------------------- - --------------------------------------- + ---------------------------|
   |      /   ___ \             /   ___ \                         1 + 3*x                              /   ___ \       |
   |     4| \/ 2  |            3| \/ 2  |                                                             2| \/ 2  |       |
   |  log |-------|         log |-------|                                                          log |-------|       |
   \      \1 + 3*x/             \1 + 3*x/                                                              \1 + 3*x/       /
------------------------------------------------------------------------------------------------------------------------
                                                                3                                                       
                                                       (1 + 3*x)                                                        
$$\frac{1}{\left(3 x + 1\right)^{3}} \left(\frac{108 \left(1 + \frac{2}{\log{\left (\frac{\sqrt{2}}{3 x + 1} \right )}}\right) \log{\left (2 \right )}}{\log^{2}{\left (\frac{\sqrt{2}}{3 x + 1} \right )}} - \frac{54 \left(1 + \frac{2}{\log{\left (\frac{\sqrt{2}}{3 x + 1} \right )}}\right) \log{\left (2 \right )}}{\log^{3}{\left (\frac{\sqrt{2}}{3 x + 1} \right )}} - \frac{54 \log{\left (2 \right )}}{\log^{4}{\left (\frac{\sqrt{2}}{3 x + 1} \right )}} - \frac{162 \sqrt{2}}{3 x + 1} \left. \frac{d}{d \xi_{2}}\left(- \frac{\log{\left (2 \right )}}{\log{\left (\xi_{2} \right )}}\right) \right|_{\substack{ \xi_{2}=\frac{\sqrt{2}}{3 x + 1} }}\right)$$