Производная 4^acot(x)

Вы ввели

 acot(x)
4       

$$4^{\operatorname{acot}{\left (x \right )}}$$

Первая производная

  acot(x)        
-4       *log(4) 
-----------------
           2     
      1 + x      

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

Вторая производная

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

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

Третья производная

         /       2          2              \       
 acot(x) |    log (4)    8*x     6*x*log(4)|       
4       *|2 - ------- - ------ - ----------|*log(4)
         |          2        2          2  |       
         \     1 + x    1 + x      1 + x   /       
---------------------------------------------------
                             2                     
                     /     2\                      
                     \1 + x /                      

$$\frac{4^{\operatorname{acot}{\left (x \right )}}}{\left(x^{2} + 1\right)^{2}} \left(- \frac{8 x^{2}}{x^{2} + 1} - \frac{6 x \log{\left (4 \right )}}{x^{2} + 1} + 2 - \frac{\log^{2}{\left (4 \right )}}{x^{2} + 1}\right) \log{\left (4 \right )}$$