Производная log(|x-1|)

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↑ Функция f () ? - производная -го порядка

Решение

Вы ввели
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log(|x - 1|)
$$\log{\left (\left|{x - 1}\right| \right )}$$
Первая производная
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             d           d              
(-1 + re(x))*--(re(x)) + --(im(x))*im(x)
             dx          dx             
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                       2                
                |x - 1|                 
$$\frac{1}{\left|{x - 1}\right|^{2}} \left(\left(\Re{x} - 1\right) \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)$$
Вторая производная
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                                                                                                                       2
                                                                             /             d           d              \ 
           2              2                  2            2                2*|(-1 + re(x))*--(re(x)) + --(im(x))*im(x)| 
/d        \    /d        \                  d            d                   \             dx          dx             / 
|--(im(x))|  + |--(re(x))|  + (-1 + re(x))*---(re(x)) + ---(im(x))*im(x) - ---------------------------------------------
\dx       /    \dx       /                   2            2                                          2                  
                                           dx           dx                                   |-1 + x|                   
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                                                               2                                                        
                                                       |-1 + x|                                                         
$$\frac{1}{\left|{x - 1}\right|^{2}} \left(- \frac{2}{\left|{x - 1}\right|^{2}} \left(\left(\Re{x} - 1\right) \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} + \left(\Re{x} - 1\right) \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right)$$
Третья производная
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                                                                                                                                                                                            /           2              2                  2            2             \
                                                                                                                                           3     /             d           d              \ |/d        \    /d        \                  d            d              |
                                                                                                 /             d           d              \    6*|(-1 + re(x))*--(re(x)) + --(im(x))*im(x)|*||--(im(x))|  + |--(re(x))|  + (-1 + re(x))*---(re(x)) + ---(im(x))*im(x)|
               3            3                              2                        2          8*|(-1 + re(x))*--(re(x)) + --(im(x))*im(x)|      \             dx          dx             / |\dx       /    \dx       /                   2            2             |
              d            d                   d          d             d          d             \             dx          dx             /                                                 \                                           dx           dx              /
(-1 + re(x))*---(re(x)) + ---(im(x))*im(x) + 3*--(im(x))*---(im(x)) + 3*--(re(x))*---(re(x)) + --------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------
               3            3                  dx          2            dx          2                                    4                                                                                    2                                                       
             dx           dx                             dx                       dx                             |-1 + x|                                                                             |-1 + x|                                                        
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                                                                                                                                      2                                                                                                                               
                                                                                                                              |-1 + x|                                                                                                                                
$$\frac{1}{\left|{x - 1}\right|^{2}} \left(\frac{8}{\left|{x - 1}\right|^{4}} \left(\left(\Re{x} - 1\right) \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} - \frac{6}{\left|{x - 1}\right|^{2}} \left(\left(\Re{x} - 1\right) \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\left(\Re{x} - 1\right) \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + \left(\Re{x} - 1\right) \frac{d^{3}}{d x^{3}} \Re{x} + \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} + 3 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 3 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x}\right)$$