Производная e^x/atan(x)

Вы ввели

    x  
   e   
-------
atan(x)

$$\frac{e^{x}}{\operatorname{atan}{\left(x \right)}}$$

  /    x  \
d |   e   |
--|-------|
dx\atan(x)/

$$\frac{d}{d x} \frac{e^{x}}{\operatorname{atan}{\left(x \right)}}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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

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