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

Производная (|x^2-x|)

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Кусочно-заданная:

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Решение

Вы ввели [src]
| 2    |
|x  - x|
∣x2−x∣\left|{x^{2} - x}\right|
Первая производная [src]
                         /  d             d                   d              \   /  2        2           \ /  d             d                   d              \
(-im(x) + 2*im(x)*re(x))*|- --(im(x)) + 2*--(im(x))*re(x) + 2*--(re(x))*im(x)| + \re (x) - im (x) - re(x)/*|- --(re(x)) - 2*--(im(x))*im(x) + 2*--(re(x))*re(x)|
                         \  dx            dx                  dx             /                             \  dx            dx                  dx             /
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                                                                            | 2    |                                                                            
                                                                            |x  - x|
1∣x2−x∣((2ℜxℑx−ℑx)(2ℜxddxℑx+2ℑxddxℜx−ddxℑx)+(2ℜxddxℜx−2ℑxddxℑx−ddxℜx)((ℜx)2−ℜx−(ℑx)2))\frac{1}{\left|{x^{2} - x}\right|} \left(\left(2 \Re{x} \Im{x} - \Im{x}\right) \left(2 \Re{x} \frac{d}{d x} \Im{x} + 2 \Im{x} \frac{d}{d x} \Re{x} - \frac{d}{d x} \Im{x}\right) + \left(2 \Re{x} \frac{d}{d x} \Re{x} - 2 \Im{x} \frac{d}{d x} \Im{x} - \frac{d}{d x} \Re{x}\right) \left(\left(\Re{x}\right)^{2} - \Re{x} - \left(\Im{x}\right)^{2}\right)\right)
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Вторая производная [src]
                                                                                                                                                                                                                                                                                                                                                                                                       2                                                                                                        
                                                                                                                                                                                                                                         //  2        2           \ /    d                   d                 d        \                  /  d             d                   d              \      \                                                                                                         
                                                     2                                                        2                             /               2                2       2                    2                  2       \   |\im (x) - re (x) + re(x)/*|- 2*--(re(x))*re(x) + 2*--(im(x))*im(x) + --(re(x))| + (-1 + 2*re(x))*|- --(im(x)) + 2*--(im(x))*re(x) + 2*--(re(x))*im(x)|*im(x)|                   /    2              2                    2                                     \      
/  d             d                   d              \    /    d                   d                 d        \    /  2        2           \ |    /d        \      /d        \       d                    d                  d        |   \                          \    dx                  dx                dx       /                  \  dx            dx                  dx             /      /                   |   d              d                    d                   d         d        |      
|- --(im(x)) + 2*--(im(x))*re(x) + 2*--(re(x))*im(x)|  + |- 2*--(re(x))*re(x) + 2*--(im(x))*im(x) + --(re(x))|  + \im (x) - re (x) + re(x)/*|- 2*|--(re(x))|  + 2*|--(im(x))|  - 2*---(re(x))*re(x) + 2*---(im(x))*im(x) + ---(re(x))| - --------------------------------------------------------------------------------------------------------------------------------------------------------------- + (-1 + 2*re(x))*|- ---(im(x)) + 2*---(im(x))*re(x) + 2*---(re(x))*im(x) + 4*--(im(x))*--(re(x))|*im(x)
\  dx            dx                  dx             /    \    dx                  dx                dx       /                              |    \dx       /      \dx       /        2                    2                  2       |                                                                                        2                                                                                           |    2              2                    2                  dx        dx       |      
                                                                                                                                            \                                      dx                   dx                 dx        /                                                                            |x*(-1 + x)|                                                                                            \  dx             dx                   dx                                      /      
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                                                                                                                                                                                                                                                  |x*(-1 + x)|
1∣x(x−1)∣(−1∣x(x−1)∣2((2ℜx−1)(2ℜxddxℑx+2ℑxddxℜx−ddxℑx)ℑx+(−2ℜxddxℜx+2ℑxddxℑx+ddxℜx)(−(ℜx)2+ℜx+(ℑx)2))2+(2ℜx−1)(2ℜxd2dx2ℑx+2ℑxd2dx2ℜx+4ddxℜxddxℑx−d2dx2ℑx)ℑx+(−2ℜxddxℜx+2ℑxddxℑx+ddxℜx)2+(2ℜxddxℑx+2ℑxddxℜx−ddxℑx)2+(−(ℜx)2+ℜx+(ℑx)2)(−2ℜxd2dx2ℜx+2ℑxd2dx2ℑx−2ddxℜx2+2ddxℑx2+d2dx2ℜx))\frac{1}{\left|{x \left(x - 1\right)}\right|} \left(- \frac{1}{\left|{x \left(x - 1\right)}\right|^{2}} \left(\left(2 \Re{x} - 1\right) \left(2 \Re{x} \frac{d}{d x} \Im{x} + 2 \Im{x} \frac{d}{d x} \Re{x} - \frac{d}{d x} \Im{x}\right) \Im{x} + \left(- 2 \Re{x} \frac{d}{d x} \Re{x} + 2 \Im{x} \frac{d}{d x} \Im{x} + \frac{d}{d x} \Re{x}\right) \left(- \left(\Re{x}\right)^{2} + \Re{x} + \left(\Im{x}\right)^{2}\right)\right)^{2} + \left(2 \Re{x} - 1\right) \left(2 \Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + 2 \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} + 4 \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} - \frac{d^{2}}{d x^{2}} \Im{x}\right) \Im{x} + \left(- 2 \Re{x} \frac{d}{d x} \Re{x} + 2 \Im{x} \frac{d}{d x} \Im{x} + \frac{d}{d x} \Re{x}\right)^{2} + \left(2 \Re{x} \frac{d}{d x} \Im{x} + 2 \Im{x} \frac{d}{d x} \Re{x} - \frac{d}{d x} \Im{x}\right)^{2} + \left(- \left(\Re{x}\right)^{2} + \Re{x} + \left(\Im{x}\right)^{2}\right) \left(- 2 \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} - 2 \frac{d}{d x} \Re{x}^{2} + 2 \frac{d}{d x} \Im{x}^{2} + \frac{d^{2}}{d x^{2}} \Re{x}\right)\right)
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Третья производная [src]
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              /                                                     2                                                        2                             /               2                2       2                    2                  2       \                  /    2              2                    2                                     \      \
                                                                                                                                                                                                                                                                                                       3                                                                                                                                                                                                                                                                                                                                                                                                                                       //  2        2           \ /    d                   d                 d        \                  /  d             d                   d              \      \ |/  d             d                   d              \    /    d                   d                 d        \    /  2        2           \ |    /d        \      /d        \       d                    d                  d        |                  |   d              d                    d                   d         d        |      |
                                                                                                                                         //  2        2           \ /    d                   d                 d        \                  /  d             d                   d              \      \                                                                                                                                                                                                                                                                                                                                                                                                                                      3*|\im (x) - re (x) + re(x)/*|- 2*--(re(x))*re(x) + 2*--(im(x))*im(x) + --(re(x))| + (-1 + 2*re(x))*|- --(im(x)) + 2*--(im(x))*re(x) + 2*--(re(x))*im(x)|*im(x)|*||- --(im(x)) + 2*--(im(x))*re(x) + 2*--(re(x))*im(x)|  + |- 2*--(re(x))*re(x) + 2*--(im(x))*im(x) + --(re(x))|  + \im (x) - re (x) + re(x)/*|- 2*|--(re(x))|  + 2*|--(im(x))|  - 2*---(re(x))*re(x) + 2*---(im(x))*im(x) + ---(re(x))| + (-1 + 2*re(x))*|- ---(im(x)) + 2*---(im(x))*re(x) + 2*---(re(x))*im(x) + 4*--(im(x))*--(re(x))|*im(x)|
                          /                2              3                    3                              2            3       \   3*|\im (x) - re (x) + re(x)/*|- 2*--(re(x))*re(x) + 2*--(im(x))*im(x) + --(re(x))| + (-1 + 2*re(x))*|- --(im(x)) + 2*--(im(x))*re(x) + 2*--(re(x))*im(x)|*im(x)|                                                            /    2              2                    2                                     \                                                           /               2                2       2                    2                  2       \                  /    3              3                    3                              2                        2       \           \                          \    dx                  dx                dx       /                  \  dx            dx                  dx             /      / |\  dx            dx                  dx             /    \    dx                  dx                dx       /                              |    \dx       /      \dx       /        2                    2                  2       |                  |    2              2                    2                  dx        dx       |      |
/  2        2           \ |    d          d              d                    d                   d          d            d        |     \                          \    dx                  dx                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        |                                                                                                                                                                          \                                                                                                                                            \                                      dx                   dx                 dx        /                  \  dx             dx                   dx                                      /      /
\im (x) - re (x) + re(x)/*|- 6*--(re(x))*---(re(x)) - 2*---(re(x))*re(x) + 2*---(im(x))*im(x) + 6*--(im(x))*---(im(x)) + ---(re(x))| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------- + 3*|- --(im(x)) + 2*--(im(x))*re(x) + 2*--(re(x))*im(x)|*|- ---(im(x)) + 2*---(im(x))*re(x) + 2*---(re(x))*im(x) + 4*--(im(x))*--(re(x))| + 3*|- 2*--(re(x))*re(x) + 2*--(im(x))*im(x) + --(re(x))|*|- 2*|--(re(x))|  + 2*|--(im(x))|  - 2*---(re(x))*re(x) + 2*---(im(x))*im(x) + ---(re(x))| + (-1 + 2*re(x))*|- ---(im(x)) + 2*---(im(x))*re(x) + 2*---(re(x))*im(x) + 6*--(im(x))*---(re(x)) + 6*--(re(x))*---(im(x))|*im(x) - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                          |    dx          2              3                    3                  dx          2            3       |                                                                                         4                                                                               \  dx            dx                  dx             / |    2              2                    2                  dx        dx       |     \    dx                  dx                dx       / |    \dx       /      \dx       /        2                    2                  2       |                  |    3              3                    3                  dx          2            dx          2       |                                                                                                                                                                                                                                                                       2                                                                                                                                                                                                                                                  
                          \              dx             dx                   dx                             dx           dx        /                                                                             |x*(-1 + x)|                                                                                                                                      \  dx             dx                   dx                                      /                                                           \                                      dx                   dx                 dx        /                  \  dx             dx                   dx                             dx                       dx        /                                                                                                                                                                                                                                                           |x*(-1 + x)|                                                                                                                                                                                                                                                   
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |x*(-1 + x)|
1∣x(x−1)∣(3∣x(x−1)∣4((2ℜx−1)(2ℜxddxℑx+2ℑxddxℜx−ddxℑx)ℑx+(−2ℜxddxℜx+2ℑxddxℑx+ddxℜx)(−(ℜx)2+ℜx+(ℑx)2))3−3∣x(x−1)∣2((2ℜx−1)(2ℜxddxℑx+2ℑxddxℜx−ddxℑx)ℑx+(−2ℜxddxℜx+2ℑxddxℑx+ddxℜx)(−(ℜx)2+ℜx+(ℑx)2))((2ℜx−1)(2ℜxd2dx2ℑx+2ℑxd2dx2ℜx+4ddxℜxddxℑx−d2dx2ℑx)ℑx+(−2ℜxddxℜx+2ℑxddxℑx+ddxℜx)2+(2ℜxddxℑx+2ℑxddxℜx−ddxℑx)2+(−(ℜx)2+ℜx+(ℑx)2)(−2ℜxd2dx2ℜx+2ℑxd2dx2ℑx−2ddxℜx2+2ddxℑx2+d2dx2ℜx))+(2ℜx−1)(2ℜxd3dx3ℑx+2ℑxd3dx3ℜx+6ddxℜxd2dx2ℑx+6ddxℑxd2dx2ℜx−d3dx3ℑx)ℑx+3(−2ℜxddxℜx+2ℑxddxℑx+ddxℜx)(−2ℜxd2dx2ℜx+2ℑxd2dx2ℑx−2ddxℜx2+2ddxℑx2+d2dx2ℜx)+3(2ℜxddxℑx+2ℑxddxℜx−ddxℑx)(2ℜxd2dx2ℑx+2ℑxd2dx2ℜx+4ddxℜxddxℑx−d2dx2ℑx)+(−(ℜx)2+ℜx+(ℑx)2)(−2ℜxd3dx3ℜx+2ℑxd3dx3ℑx−6ddxℜxd2dx2ℜx+6ddxℑxd2dx2ℑx+d3dx3ℜx))\frac{1}{\left|{x \left(x - 1\right)}\right|} \left(\frac{3}{\left|{x \left(x - 1\right)}\right|^{4}} \left(\left(2 \Re{x} - 1\right) \left(2 \Re{x} \frac{d}{d x} \Im{x} + 2 \Im{x} \frac{d}{d x} \Re{x} - \frac{d}{d x} \Im{x}\right) \Im{x} + \left(- 2 \Re{x} \frac{d}{d x} \Re{x} + 2 \Im{x} \frac{d}{d x} \Im{x} + \frac{d}{d x} \Re{x}\right) \left(- \left(\Re{x}\right)^{2} + \Re{x} + \left(\Im{x}\right)^{2}\right)\right)^{3} - \frac{3}{\left|{x \left(x - 1\right)}\right|^{2}} \left(\left(2 \Re{x} - 1\right) \left(2 \Re{x} \frac{d}{d x} \Im{x} + 2 \Im{x} \frac{d}{d x} \Re{x} - \frac{d}{d x} \Im{x}\right) \Im{x} + \left(- 2 \Re{x} \frac{d}{d x} \Re{x} + 2 \Im{x} \frac{d}{d x} \Im{x} + \frac{d}{d x} \Re{x}\right) \left(- \left(\Re{x}\right)^{2} + \Re{x} + \left(\Im{x}\right)^{2}\right)\right) \left(\left(2 \Re{x} - 1\right) \left(2 \Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + 2 \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} + 4 \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} - \frac{d^{2}}{d x^{2}} \Im{x}\right) \Im{x} + \left(- 2 \Re{x} \frac{d}{d x} \Re{x} + 2 \Im{x} \frac{d}{d x} \Im{x} + \frac{d}{d x} \Re{x}\right)^{2} + \left(2 \Re{x} \frac{d}{d x} \Im{x} + 2 \Im{x} \frac{d}{d x} \Re{x} - \frac{d}{d x} \Im{x}\right)^{2} + \left(- \left(\Re{x}\right)^{2} + \Re{x} + \left(\Im{x}\right)^{2}\right) \left(- 2 \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} - 2 \frac{d}{d x} \Re{x}^{2} + 2 \frac{d}{d x} \Im{x}^{2} + \frac{d^{2}}{d x^{2}} \Re{x}\right)\right) + \left(2 \Re{x} - 1\right) \left(2 \Re{x} \frac{d^{3}}{d x^{3}} \Im{x} + 2 \Im{x} \frac{d^{3}}{d x^{3}} \Re{x} + 6 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + 6 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} - \frac{d^{3}}{d x^{3}} \Im{x}\right) \Im{x} + 3 \left(- 2 \Re{x} \frac{d}{d x} \Re{x} + 2 \Im{x} \frac{d}{d x} \Im{x} + \frac{d}{d x} \Re{x}\right) \left(- 2 \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} - 2 \frac{d}{d x} \Re{x}^{2} + 2 \frac{d}{d x} \Im{x}^{2} + \frac{d^{2}}{d x^{2}} \Re{x}\right) + 3 \left(2 \Re{x} \frac{d}{d x} \Im{x} + 2 \Im{x} \frac{d}{d x} \Re{x} - \frac{d}{d x} \Im{x}\right) \left(2 \Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + 2 \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} + 4 \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} - \frac{d^{2}}{d x^{2}} \Im{x}\right) + \left(- \left(\Re{x}\right)^{2} + \Re{x} + \left(\Im{x}\right)^{2}\right) \left(- 2 \Re{x} \frac{d^{3}}{d x^{3}} \Re{x} + 2 \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} - 6 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 6 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d^{3}}{d x^{3}} \Re{x}\right)\right)
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