Производная e^(1/atan(x))

Вы ввели

    1   
 -------
 atan(x)
E       

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

                                                                                                                    1   
/                            2                                                                                \  -------
|            1            8*x             6                   6                 12*x                6*x       |  atan(x)
|2 - ----------------- - ------ - ----------------- - ----------------- - ---------------- - -----------------|*e       
|    /     2\     4           2   /     2\     3      /     2\     2      /     2\           /     2\     2   |         
\    \1 + x /*atan (x)   1 + x    \1 + x /*atan (x)   \1 + x /*atan (x)   \1 + x /*atan(x)   \1 + x /*atan (x)/         
------------------------------------------------------------------------------------------------------------------------
                                                           2                                                            
                                                   /     2\      2                                                      
                                                   \1 + x / *atan (x)                                                   

$$\frac{e^{\frac{1}{\operatorname{atan}{\left (x \right )}}}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left (x \right )}} \left(- \frac{8 x^{2}}{x^{2} + 1} - \frac{12 x}{\left(x^{2} + 1\right) \operatorname{atan}{\left (x \right )}} - \frac{6 x}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left (x \right )}} + 2 - \frac{6}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left (x \right )}} - \frac{6}{\left(x^{2} + 1\right) \operatorname{atan}^{3}{\left (x \right )}} - \frac{1}{\left(x^{2} + 1\right) \operatorname{atan}^{4}{\left (x \right )}}\right)$$