Производная 1/atan(x)

Вы ввели

     1   
1*-------
  atan(x)

$$1 \cdot \frac{1}{\operatorname{atan}{\left(x \right)}}$$

d /     1   \
--|1*-------|
dx\  atan(x)/

$$\frac{d}{d x} 1 \cdot \frac{1}{\operatorname{atan}{\left(x \right)}}$$

Первая производная

       -1        
-----------------
/     2\     2   
\1 + x /*atan (x)

$$- \frac{1}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}}$$

Вторая производная

   /       1   \  
 2*|x + -------|  
   \    atan(x)/  
------------------
        2         
/     2\      2   
\1 + x / *atan (x)

$$\frac{2 \left(x + \frac{1}{\operatorname{atan}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}}$$

Третья производная

   /                             2                    \
   |             3            4*x           6*x       |
-2*|-1 + ----------------- + ------ + ----------------|
   |     /     2\     2           2   /     2\        |
   \     \1 + x /*atan (x)   1 + x    \1 + x /*atan(x)/
-------------------------------------------------------
                           2                           
                   /     2\      2                     
                   \1 + x / *atan (x)                  

$$- \frac{2 \cdot \left(\frac{4 x^{2}}{x^{2} + 1} + \frac{6 x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - 1 + \frac{3}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}}$$

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