Производная 3^atan(2*x)

Вы ввели

 atan(2*x)
3         

$$3^{\operatorname{atan}{\left (2 x \right )}}$$

Первая производная

   atan(2*x)       
2*3         *log(3)
-------------------
             2     
      1 + 4*x      

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

Вторая производная

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

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

Третья производная

             /        2            2                \       
   atan(2*x) |     log (3)     32*x      12*x*log(3)|       
8*3         *|-2 + -------- + -------- - -----------|*log(3)
             |            2          2            2 |       
             \     1 + 4*x    1 + 4*x      1 + 4*x  /       
------------------------------------------------------------
                                  2                         
                        /       2\                          
                        \1 + 4*x /                          

$$\frac{8 \cdot 3^{\operatorname{atan}{\left (2 x \right )}}}{\left(4 x^{2} + 1\right)^{2}} \left(\frac{32 x^{2}}{4 x^{2} + 1} - \frac{12 x \log{\left (3 \right )}}{4 x^{2} + 1} - 2 + \frac{\log^{2}{\left (3 \right )}}{4 x^{2} + 1}\right) \log{\left (3 \right )}$$