Производная 5^(atan(3*x))

Вы ввели

 atan(3*x)
5         

$$5^{\operatorname{atan}{\left (3 x \right )}}$$

Первая производная

   atan(3*x)       
3*5         *log(5)
-------------------
             2     
      1 + 9*x      

$$\frac{3 \cdot 5^{\operatorname{atan}{\left (3 x \right )}}}{9 x^{2} + 1} \log{\left (5 \right )}$$

Вторая производная

   atan(3*x)                       
9*5         *(-6*x + log(5))*log(5)
-----------------------------------
                      2            
            /       2\             
            \1 + 9*x /             

$$\frac{9 \cdot 5^{\operatorname{atan}{\left (3 x \right )}}}{\left(9 x^{2} + 1\right)^{2}} \left(- 6 x + \log{\left (5 \right )}\right) \log{\left (5 \right )}$$

Третья производная

              /        2            2                \       
    atan(3*x) |     log (5)     72*x      18*x*log(5)|       
27*5         *|-2 + -------- + -------- - -----------|*log(5)
              |            2          2            2 |       
              \     1 + 9*x    1 + 9*x      1 + 9*x  /       
-------------------------------------------------------------
                                   2                         
                         /       2\                          
                         \1 + 9*x /                          

$$\frac{27 \cdot 5^{\operatorname{atan}{\left (3 x \right )}}}{\left(9 x^{2} + 1\right)^{2}} \left(\frac{72 x^{2}}{9 x^{2} + 1} - \frac{18 x \log{\left (5 \right )}}{9 x^{2} + 1} - 2 + \frac{\log^{2}{\left (5 \right )}}{9 x^{2} + 1}\right) \log{\left (5 \right )}$$