Производная atan(x+1)+(x+1)/(x^2+2*x+2)

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↑ Функция f () ? - производная -го порядка

Решение

Вы ввели
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                 x + 1    
atan(x + 1) + ------------
               2          
              x  + 2*x + 2
$$\frac{x + 1}{x^{2} + 2 x + 2} + \operatorname{atan}{\left (x + 1 \right )}$$
График
Первая производная
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     1              1         (-2 - 2*x)*(x + 1)
------------ + ------------ + ------------------
           2    2                            2  
1 + (x + 1)    x  + 2*x + 2    / 2          \   
                               \x  + 2*x + 2/   
$$\frac{\left(- 2 x - 2\right) \left(x + 1\right)}{\left(x^{2} + 2 x + 2\right)^{2}} + \frac{1}{x^{2} + 2 x + 2} + \frac{1}{\left(x + 1\right)^{2} + 1}$$
Вторая производная
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          /                                                  2  \
          |         1                 3             4*(1 + x)   |
2*(1 + x)*|- --------------- - --------------- + ---------------|
          |                2                 2                 3|
          |  /           2\    /     2      \    /     2      \ |
          \  \1 + (1 + x) /    \2 + x  + 2*x/    \2 + x  + 2*x/ /
$$2 \left(x + 1\right) \left(\frac{4 \left(x + 1\right)^{2}}{\left(x^{2} + 2 x + 2\right)^{3}} - \frac{3}{\left(x^{2} + 2 x + 2\right)^{2}} - \frac{1}{\left(\left(x + 1\right)^{2} + 1\right)^{2}}\right)$$
Третья производная
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  /                                                  4                 2                 2  \
  |         1                 3            24*(1 + x)         4*(1 + x)        24*(1 + x)   |
2*|- --------------- - --------------- - --------------- + --------------- + ---------------|
  |                2                 2                 4                 3                 3|
  |  /           2\    /     2      \    /     2      \    /           2\    /     2      \ |
  \  \1 + (1 + x) /    \2 + x  + 2*x/    \2 + x  + 2*x/    \1 + (1 + x) /    \2 + x  + 2*x/ /
$$2 \left(- \frac{24 \left(x + 1\right)^{4}}{\left(x^{2} + 2 x + 2\right)^{4}} + \frac{24 \left(x + 1\right)^{2}}{\left(x^{2} + 2 x + 2\right)^{3}} + \frac{4 \left(x + 1\right)^{2}}{\left(\left(x + 1\right)^{2} + 1\right)^{3}} - \frac{3}{\left(x^{2} + 2 x + 2\right)^{2}} - \frac{1}{\left(\left(x + 1\right)^{2} + 1\right)^{2}}\right)$$