Производная 5^atan(x)

Вы ввели

 atan(x)
5       

$$5^{\operatorname{atan}{\left (x \right )}}$$

Первая производная

 atan(x)       
5       *log(5)
---------------
          2    
     1 + x     

$$\frac{5^{\operatorname{atan}{\left (x \right )}}}{x^{2} + 1} \log{\left (5 \right )}$$

Вторая производная

 atan(x)                       
5       *(-2*x + log(5))*log(5)
-------------------------------
                   2           
           /     2\            
           \1 + x /            

$$\frac{5^{\operatorname{atan}{\left (x \right )}}}{\left(x^{2} + 1\right)^{2}} \left(- 2 x + \log{\left (5 \right )}\right) \log{\left (5 \right )}$$

Третья производная

         /        2          2              \       
 atan(x) |     log (5)    8*x     6*x*log(5)|       
5       *|-2 + ------- + ------ - ----------|*log(5)
         |           2        2          2  |       
         \      1 + x    1 + x      1 + x   /       
----------------------------------------------------
                             2                      
                     /     2\                       
                     \1 + x /                       

$$\frac{5^{\operatorname{atan}{\left (x \right )}}}{\left(x^{2} + 1\right)^{2}} \left(\frac{8 x^{2}}{x^{2} + 1} - \frac{6 x \log{\left (5 \right )}}{x^{2} + 1} - 2 + \frac{\log^{2}{\left (5 \right )}}{x^{2} + 1}\right) \log{\left (5 \right )}$$