Производная 5^x*atan(x)

Вы ввели

 x        
5 *atan(x)

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

   /                                     2            2               \
 x |      2          3              3*log (5)      8*x      6*x*log(5)|
5 *|- --------- + log (5)*atan(x) + --------- + --------- - ----------|
   |          2                            2            3           2 |
   |  /     2\                        1 + x     /     2\    /     2\  |
   \  \1 + x /                                  \1 + x /    \1 + x /  /

$$5^{x} \left(\frac{8 x^{2}}{\left(x^{2} + 1\right)^{3}} - \frac{6 x \log{\left (5 \right )}}{\left(x^{2} + 1\right)^{2}} + \log^{3}{\left (5 \right )} \operatorname{atan}{\left (x \right )} + \frac{3 \log^{2}{\left (5 \right )}}{x^{2} + 1} - \frac{2}{\left(x^{2} + 1\right)^{2}}\right)$$