Производная функции/ От одной переменной/ y' = ((|1-x^2|))'

Производная (|1-x^2|)

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Кусочно-заданная:

{ кусочно-заданную функцию ввести здесь.

Решение

Вы ввели [src]
|     2|
|1 - x |
∣−x2+1∣\left|{- x^{2} + 1}\right|
Первая производная [src]
/    d                   d              \ /      2        2   \     /    d                   d              \            
|- 2*--(re(x))*re(x) + 2*--(im(x))*im(x)|*\1 + im (x) - re (x)/ - 2*|- 2*--(im(x))*re(x) - 2*--(re(x))*im(x)|*im(x)*re(x)
\    dx                  dx             /                           \    dx                  dx             /            
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                                                        |      2|                                                        
                                                        |-1 + x |
1∣x2−1∣((−2ℜxddxℜx+2ℑxddxℑx)(−(ℜx)2+(ℑx)2+1)−2(−2ℜxddxℑx−2ℑxddxℜx)ℜxℑx)\frac{1}{\left|{x^{2} - 1}\right|} \left(\left(- 2 \Re{x} \frac{d}{d x} \Re{x} + 2 \Im{x} \frac{d}{d x} \Im{x}\right) \left(- \left(\Re{x}\right)^{2} + \left(\Im{x}\right)^{2} + 1\right) - 2 \left(- 2 \Re{x} \frac{d}{d x} \Im{x} - 2 \Im{x} \frac{d}{d x} \Re{x}\right) \Re{x} \Im{x}\right)
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Вторая производная [src]
  /                                                                                                                                                                                                                                                      2                                                                                                                                                                                              \
  |                                                                                                                                       //d                 d              \ /      2        2   \     /d                 d              \            \                                                                                                                                                                                               |
  |                                     2                         /           2              2     2                  2             \   2*||--(re(x))*re(x) - --(im(x))*im(x)|*\1 + im (x) - re (x)/ - 2*|--(im(x))*re(x) + --(re(x))*im(x)|*im(x)*re(x)|                                                                                                                      /  2                  2                                     \            |
  |  /d                 d              \    /      2        2   \ |/d        \    /d        \     d                  d              |     \\dx                dx             /                           \dx                dx             /            /      /d                 d              \ d                   /d                 d              \ d                   | d                  d                   d         d        |            |
2*|2*|--(re(x))*re(x) - --(im(x))*im(x)|  - \1 + im (x) - re (x)/*||--(re(x))|  - |--(im(x))|  + ---(re(x))*re(x) - ---(im(x))*im(x)| - ------------------------------------------------------------------------------------------------------------------ + 2*|--(im(x))*re(x) + --(re(x))*im(x)|*--(im(x))*re(x) + 2*|--(im(x))*re(x) + --(re(x))*im(x)|*--(re(x))*im(x) + 2*|---(im(x))*re(x) + ---(re(x))*im(x) + 2*--(im(x))*--(re(x))|*im(x)*re(x)|
  |  \dx                dx             /                          |\dx       /    \dx       /      2                  2             |                                                                2                                                         \dx                dx             / dx                  \dx                dx             / dx                  |  2                  2                  dx        dx       |            |
  |                                                               \                              dx                 dx              /                                                       |      2|                                                                                                                                                                          \dx                 dx                                      /            |
  \                                                                                                                                                                                         |-1 + x |                                                                                                                                                                                                                                                   /
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                                                                                                                                                                                                                        |      2|                                                                                                                                                                                                                        
                                                                                                                                                                                                                        |-1 + x |
1∣x2−1∣(−4∣x2−1∣2((ℜxddxℜx−ℑxddxℑx)(−(ℜx)2+(ℑx)2+1)−2(ℜxddxℑx+ℑxddxℜx)ℜxℑx)2+4(ℜxddxℜx−ℑxddxℑx)2+4(ℜxddxℑx+ℑxddxℜx)ℜxddxℑx+4(ℜxddxℑx+ℑxddxℜx)ℑxddxℜx+4(ℜxd2dx2ℑx+ℑxd2dx2ℜx+2ddxℜxddxℑx)ℜxℑx−2(−(ℜx)2+(ℑx)2+1)(ℜxd2dx2ℜx−ℑxd2dx2ℑx+ddxℜx2−ddxℑx2))\frac{1}{\left|{x^{2} - 1}\right|} \left(- \frac{4}{\left|{x^{2} - 1}\right|^{2}} \left(\left(\Re{x} \frac{d}{d x} \Re{x} - \Im{x} \frac{d}{d x} \Im{x}\right) \left(- \left(\Re{x}\right)^{2} + \left(\Im{x}\right)^{2} + 1\right) - 2 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \Re{x} \Im{x}\right)^{2} + 4 \left(\Re{x} \frac{d}{d x} \Re{x} - \Im{x} \frac{d}{d x} \Im{x}\right)^{2} + 4 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \Re{x} \frac{d}{d x} \Im{x} + 4 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \Im{x} \frac{d}{d x} \Re{x} + 4 \left(\Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}\right) \Re{x} \Im{x} - 2 \left(- \left(\Re{x}\right)^{2} + \left(\Im{x}\right)^{2} + 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)
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Третья производная [src]
  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                     2                         /           2              2     2                  2             \                                                                                                                     /  2                  2                                     \            \\
  |                                                                                                                                                                                                                                    3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           //d                 d              \ /      2        2   \     /d                 d              \            \ |  /d                 d              \    /      2        2   \ |/d        \    /d        \     d                  d              |     /d                 d              \ d                   /d                 d              \ d                   | d                  d                   d         d        |            ||
  |                                                                                                                     //d                 d              \ /      2        2   \     /d                 d              \            \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          6*||--(re(x))*re(x) - --(im(x))*im(x)|*\1 + im (x) - re (x)/ - 2*|--(im(x))*re(x) + --(re(x))*im(x)|*im(x)*re(x)|*|2*|--(re(x))*re(x) - --(im(x))*im(x)|  - \1 + im (x) - re (x)/*||--(re(x))|  - |--(im(x))|  + ---(re(x))*re(x) - ---(im(x))*im(x)| + 2*|--(im(x))*re(x) + --(re(x))*im(x)|*--(im(x))*re(x) + 2*|--(im(x))*re(x) + --(re(x))*im(x)|*--(re(x))*im(x) + 2*|---(im(x))*re(x) + ---(re(x))*im(x) + 2*--(im(x))*--(re(x))|*im(x)*re(x)||
  |                        /  3                  3                              2                        2       \   12*||--(re(x))*re(x) - --(im(x))*im(x)|*\1 + im (x) - re (x)/ - 2*|--(im(x))*re(x) + --(re(x))*im(x)|*im(x)*re(x)|                                          /           2              2     2                  2             \                                           2                                                        2                  /  3                  3                              2                        2       \                                                                             /  2                  2                                     \                     /  2                  2                                     \                     \\dx                dx             /                           \dx                dx             /            / |  \dx                dx             /                          |\dx       /    \dx       /      2                  2             |     \dx                dx             / dx                  \dx                dx             / dx                  |  2                  2                  dx        dx       |            ||
  |  /      2        2   \ | d                  d                   d          d             d          d        |      \\dx                dx             /                           \dx                dx             /            /      /d                 d              \ |/d        \    /d        \     d                  d              |     /d                 d              \  d                   /d                 d              \  d                   | d                  d                   d          d             d          d        |                 /d                 d              \ d         d             | d                  d                   d         d        | d                   | d                  d                   d         d        | d                                                                                                                                   \                                                               \                              dx                 dx              /                                                                                                                     \dx                 dx                                      /            /|
2*|- \1 + im (x) - re (x)/*|---(re(x))*re(x) - ---(im(x))*im(x) - 3*--(im(x))*---(im(x)) + 3*--(re(x))*---(re(x))| - ------------------------------------------------------------------------------------------------------------------- + 6*|--(re(x))*re(x) - --(im(x))*im(x)|*||--(re(x))|  - |--(im(x))|  + ---(re(x))*re(x) - ---(im(x))*im(x)| + 2*|--(im(x))*re(x) + --(re(x))*im(x)|*---(im(x))*re(x) + 2*|--(im(x))*re(x) + --(re(x))*im(x)|*---(re(x))*im(x) + 2*|---(im(x))*re(x) + ---(re(x))*im(x) + 3*--(im(x))*---(re(x)) + 3*--(re(x))*---(im(x))|*im(x)*re(x) + 4*|--(im(x))*re(x) + --(re(x))*im(x)|*--(im(x))*--(re(x)) + 4*|---(im(x))*re(x) + ---(re(x))*im(x) + 2*--(im(x))*--(re(x))|*--(im(x))*re(x) + 4*|---(im(x))*re(x) + ---(re(x))*im(x) + 2*--(im(x))*--(re(x))|*--(re(x))*im(x) + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  |                        |  3                  3                  dx          2            dx          2       |                                                                 4                                                         \dx                dx             / |\dx       /    \dx       /      2                  2             |     \dx                dx             /   2                  \dx                dx             /   2                  |  3                  3                  dx          2            dx          2       |                 \dx                dx             / dx        dx            |  2                  2                  dx        dx       | dx                  |  2                  2                  dx        dx       | dx                                                                                                                                                                                                                                              2                                                                                                                                                                                                                     |
  |                        \dx                 dx                             dx                       dx        /                                                        |      2|                                                                                              \                              dx                 dx              /                                         dx                                                       dx                   \dx                 dx                             dx                       dx        /                                                                             \dx                 dx                                      /                     \dx                 dx                                      /                                                                                                                                                                                                                                        |      2|                                                                                                                                                                                                                      |
  \                                                                                                                                                                       |-1 + x |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |-1 + x |                                                                                                                                                                                                                      /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |      2|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |-1 + x |
1∣x2−1∣(−24∣x2−1∣4((ℜxddxℜx−ℑxddxℑx)(−(ℜx)2+(ℑx)2+1)−2(ℜxddxℑx+ℑxddxℜx)ℜxℑx)3+12∣x2−1∣2((ℜxddxℜx−ℑxddxℑx)(−(ℜx)2+(ℑx)2+1)−2(ℜxddxℑx+ℑxddxℜx)ℜxℑx)(2(ℜxddxℜx−ℑxddxℑx)2+2(ℜxddxℑx+ℑxddxℜx)ℜxddxℑx+2(ℜxddxℑx+ℑxddxℜx)ℑxddxℜx+2(ℜxd2dx2ℑx+ℑxd2dx2ℜx+2ddxℜxddxℑx)ℜxℑx−(−(ℜx)2+(ℑx)2+1)(ℜxd2dx2ℜx−ℑxd2dx2ℑx+ddxℜx2−ddxℑx2))+12(ℜxddxℜx−ℑxddxℑx)(ℜxd2dx2ℜx−ℑxd2dx2ℑx+ddxℜx2−ddxℑx2)+4(ℜxddxℑx+ℑxddxℜx)ℜxd2dx2ℑx+4(ℜxddxℑx+ℑxddxℜx)ℑxd2dx2ℜx+8(ℜxddxℑx+ℑxddxℜx)ddxℜxddxℑx+8(ℜxd2dx2ℑx+ℑxd2dx2ℜx+2ddxℜxddxℑx)ℜxddxℑx+8(ℜxd2dx2ℑx+ℑxd2dx2ℜx+2ddxℜxddxℑx)ℑxddxℜx−2(−(ℜx)2+(ℑx)2+1)(ℜxd3dx3ℜx−ℑxd3dx3ℑx+3ddxℜxd2dx2ℜx−3ddxℑxd2dx2ℑx)+4(ℜxd3dx3ℑx+ℑxd3dx3ℜx+3ddxℜxd2dx2ℑx+3ddxℑxd2dx2ℜx)ℜxℑx)\frac{1}{\left|{x^{2} - 1}\right|} \left(- \frac{24}{\left|{x^{2} - 1}\right|^{4}} \left(\left(\Re{x} \frac{d}{d x} \Re{x} - \Im{x} \frac{d}{d x} \Im{x}\right) \left(- \left(\Re{x}\right)^{2} + \left(\Im{x}\right)^{2} + 1\right) - 2 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \Re{x} \Im{x}\right)^{3} + \frac{12}{\left|{x^{2} - 1}\right|^{2}} \left(\left(\Re{x} \frac{d}{d x} \Re{x} - \Im{x} \frac{d}{d x} \Im{x}\right) \left(- \left(\Re{x}\right)^{2} + \left(\Im{x}\right)^{2} + 1\right) - 2 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \Re{x} \Im{x}\right) \left(2 \left(\Re{x} \frac{d}{d x} \Re{x} - \Im{x} \frac{d}{d x} \Im{x}\right)^{2} + 2 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \Re{x} \frac{d}{d x} \Im{x} + 2 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \Im{x} \frac{d}{d x} \Re{x} + 2 \left(\Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}\right) \Re{x} \Im{x} - \left(- \left(\Re{x}\right)^{2} + \left(\Im{x}\right)^{2} + 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) + 12 \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) + 4 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + 4 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} + 8 \left(\Re{x} \frac{d}{d x} \Im{x} + \Im{x} \frac{d}{d x} \Re{x}\right) \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} + 8 \left(\Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}\right) \Re{x} \frac{d}{d x} \Im{x} + 8 \left(\Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}\right) \Im{x} \frac{d}{d x} \Re{x} - 2 \left(- \left(\Re{x}\right)^{2} + \left(\Im{x}\right)^{2} + 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) + 4 \left(\Re{x} \frac{d^{3}}{d x^{3}} \Im{x} + \Im{x} \frac{d^{3}}{d x^{3}} \Re{x} + 3 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + 3 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Re{x}\right) \Re{x} \Im{x}\right)
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