Производная 2^x*acot(x)

Вы ввели

 x        
2 *acot(x)

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

   /                                    2          2                \
 x |    2          3                 8*x      3*log (2)   6*x*log(2)|
2 *|--------- + log (2)*acot(x) - --------- - --------- + ----------|
   |        2                             3          2            2 |
   |/     2\                      /     2\      1 + x     /     2\  |
   \\1 + x /                      \1 + x /                \1 + x /  /

$$2^{x} \left(- \frac{8 x^{2}}{\left(x^{2} + 1\right)^{3}} + \frac{6 x \log{\left (2 \right )}}{\left(x^{2} + 1\right)^{2}} + \log^{3}{\left (2 \right )} \operatorname{acot}{\left (x \right )} - \frac{3 \log^{2}{\left (2 \right )}}{x^{2} + 1} + \frac{2}{\left(x^{2} + 1\right)^{2}}\right)$$