Производная ((|x|)+1)/((|x|)-3)

Вы ввели

|x| + 1
-------
|x| - 3

$$\frac{\left|{x}\right| + 1}{\left|{x}\right| - 3}$$

Первая производная

d                 d                 /d                 d              \          
--(im(x))*im(x) + --(re(x))*re(x)   |--(im(x))*im(x) + --(re(x))*re(x)|*(|x| + 1)
dx                dx                \dx                dx             /          
--------------------------------- - ---------------------------------------------
          (|x| - 3)*|x|                                      2                   
                                                    (|x| - 3) *|x|               

$$\frac{1}{\left(\left|{x}\right| - 3\right) \left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) - \frac{1}{\left(\left|{x}\right| - 3\right)^{2} \left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\left|{x}\right| + 1\right)$$

Вторая производная

                                                                                                                     /           2              2     2                  2             \                                                                                                                                             
                                                                                                       2             |/d        \    /d        \     d                  d              |                                        2                                      2                                                  2          
                                                                    /d                 d              \    (1 + |x|)*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|     /d                 d              \    /d                 d              \                /d                 d              \           
           2              2     2                  2                |--(im(x))*im(x) + --(re(x))*re(x)|              |\dx       /    \dx       /      2                  2             |   2*|--(im(x))*im(x) + --(re(x))*re(x)|    |--(im(x))*im(x) + --(re(x))*re(x)| *(1 + |x|)   2*|--(im(x))*im(x) + --(re(x))*re(x)| *(1 + |x|)
/d        \    /d        \     d                  d                 \dx                dx             /              \                              dx                 dx              /     \dx                dx             /    \dx                dx             /                \dx                dx             /           
|--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x) - ------------------------------------ - ----------------------------------------------------------------------------- - -------------------------------------- + ---------------------------------------------- + ------------------------------------------------
\dx       /    \dx       /      2                  2                                   2                                                      -3 + |x|                                                 (-3 + |x|)*|x|                                            2                                             2                     
                              dx                 dx                                 |x|                                                                                                                                                            (-3 + |x|)*|x|                                    (-3 + |x|) *|x|                 
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                            (-3 + |x|)*|x|                                                                                                                                                           

$$\frac{1}{\left(\left|{x}\right| - 3\right) \left|{x}\right|} \left(- \frac{1}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} + \frac{1}{\left(\left|{x}\right| - 3\right) \left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} \left(\left|{x}\right| + 1\right) - \frac{2}{\left(\left|{x}\right| - 3\right) \left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} + \frac{2}{\left(\left|{x}\right| - 3\right)^{2} \left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} \left(\left|{x}\right| + 1\right) + \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2} - \frac{1}{\left|{x}\right| - 3} \left(\left|{x}\right| + 1\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right)\right)$$

Третья производная

                                                                                                                                           /  3                  3                              2                        2       \                                         /           2              2     2                  2             \                                                                                                                           /           2              2     2                  2             \                                                                                                                                                                                                            /           2              2     2                  2             \                                                   /           2              2     2                  2             \
                                                                           3                                                               | d                  d                   d          d             d          d        |     /d                 d              \ |/d        \    /d        \     d                  d              |                                        3                                        3     /d                 d              \ |/d        \    /d        \     d                  d              |                                        3                                                  3                                                  3                         /d                 d              \ |/d        \    /d        \     d                  d              |               /d                 d              \ |/d        \    /d        \     d                  d              |
                                        /d                 d              \                                                      (1 + |x|)*|---(im(x))*im(x) + ---(re(x))*re(x) + 3*--(im(x))*---(im(x)) + 3*--(re(x))*---(re(x))|   3*|--(im(x))*im(x) + --(re(x))*re(x)|*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|     /d                 d              \      /d                 d              \    6*|--(im(x))*im(x) + --(re(x))*re(x)|*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|     /d                 d              \                /d                 d              \                /d                 d              \              3*(1 + |x|)*|--(im(x))*im(x) + --(re(x))*re(x)|*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|   6*(1 + |x|)*|--(im(x))*im(x) + --(re(x))*re(x)|*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|
  3                  3                3*|--(im(x))*im(x) + --(re(x))*re(x)|                  2                        2                    |  3                  3                  dx          2            dx          2       |     \dx                dx             / |\dx       /    \dx       /      2                  2             |   6*|--(im(x))*im(x) + --(re(x))*re(x)|    6*|--(im(x))*im(x) + --(re(x))*re(x)|      \dx                dx             / |\dx       /    \dx       /      2                  2             |   6*|--(im(x))*im(x) + --(re(x))*re(x)| *(1 + |x|)   6*|--(im(x))*im(x) + --(re(x))*re(x)| *(1 + |x|)   3*|--(im(x))*im(x) + --(re(x))*re(x)| *(1 + |x|)               \dx                dx             / |\dx       /    \dx       /      2                  2             |               \dx                dx             / |\dx       /    \dx       /      2                  2             |
 d                  d                   \dx                dx             /      d          d             d          d                     \dx                 dx                             dx                       dx        /                                         \                              dx                 dx              /     \dx                dx             /      \dx                dx             /                                          \                              dx                 dx              /     \dx                dx             /                \dx                dx             /                \dx                dx             /                                                              \                              dx                 dx              /                                                   \                              dx                 dx              /
---(im(x))*im(x) + ---(re(x))*re(x) + -------------------------------------- + 3*--(im(x))*---(im(x)) + 3*--(re(x))*---(re(x)) - ------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------- + -------------------------------------- + -------------------------------------- - --------------------------------------------------------------------------------------------------------- - ------------------------------------------------ - ------------------------------------------------ - ------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------
  3                  3                                    4                      dx          2            dx          2                                                       -3 + |x|                                                                                                     2                                                                              3                                    2    2                                                            (-3 + |x|)*|x|                                                                          3    2                                             2    3                                                 4                                                                                    2                                                                                                                 2                                                      
dx                 dx                                  |x|                                 dx                       dx                                                                                                                                                                  |x|                                                                 (-3 + |x|)*|x|                           (-3 + |x|) *|x|                                                                                                                                           (-3 + |x|) *|x|                                    (-3 + |x|) *|x|                                    (-3 + |x|)*|x|                                                                       (-3 + |x|)*|x|                                                                                                        (-3 + |x|) *|x|                                                  
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                  (-3 + |x|)*|x|                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

$$\frac{1}{\left(\left|{x}\right| - 3\right) \left|{x}\right|} \left(\frac{3}{\left|{x}\right|^{4}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} - \frac{3}{\left(\left|{x}\right| - 3\right) \left|{x}\right|^{4}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} \left(\left|{x}\right| + 1\right) + \frac{6}{\left(\left|{x}\right| - 3\right) \left|{x}\right|^{3}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} - \frac{6}{\left(\left|{x}\right| - 3\right)^{2} \left|{x}\right|^{3}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} \left(\left|{x}\right| + 1\right) + \frac{6}{\left(\left|{x}\right| - 3\right)^{2} \left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} - \frac{6}{\left(\left|{x}\right| - 3\right)^{3} \left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} \left(\left|{x}\right| + 1\right) - \frac{3}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + \frac{3}{\left(\left|{x}\right| - 3\right) \left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\left|{x}\right| + 1\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) - \frac{6}{\left(\left|{x}\right| - 3\right) \left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + \frac{6}{\left(\left|{x}\right| - 3\right)^{2} \left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\left|{x}\right| + 1\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + \Re{x} \frac{d^{3}}{d x^{3}} \Re{x} + \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} + 3 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 3 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} - \frac{1}{\left|{x}\right| - 3} \left(\left|{x}\right| + 1\right) \left(\Re{x} \frac{d^{3}}{d x^{3}} \Re{x} + \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} + 3 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 3 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x}\right)\right)$$