Производная ((5^cos(3*x))/sin(3*x))+atan(5*x^3)

Вы ввели

 cos(3*x)             
5               /   3\
--------- + atan\5*x /
 sin(3*x)             

$$\frac{5^{\cos{\left (3 x \right )}}}{\sin{\left (3 x \right )}} + \operatorname{atan}{\left (5 x^{3} \right )}$$

Первая производная

                             2        cos(3*x)         
     cos(3*x)            15*x      3*5        *cos(3*x)
- 3*5        *log(5) + --------- - --------------------
                               6           2           
                       1 + 25*x         sin (3*x)      

$$- 3 \cdot 5^{\cos{\left (3 x \right )}} \log{\left (5 \right )} - \frac{3 \cdot 5^{\cos{\left (3 x \right )}}}{\sin^{2}{\left (3 x \right )}} \cos{\left (3 x \right )} + \frac{15 x^{2}}{25 x^{6} + 1}$$

Вторая производная

  /          7         cos(3*x)                                                 cos(3*x)    2           cos(3*x)                \
  |     750*x       3*5              10*x        cos(3*x)    2               6*5        *cos (3*x)   3*5        *cos(3*x)*log(5)|
3*|- ------------ + ----------- + --------- + 3*5        *log (5)*sin(3*x) + --------------------- + ---------------------------|
  |             2     sin(3*x)            6                                           3                        sin(3*x)         |
  |  /        6\                  1 + 25*x                                         sin (3*x)                                    |
  \  \1 + 25*x /                                                                                                                /

$$3 \left(3 \cdot 5^{\cos{\left (3 x \right )}} \log^{2}{\left (5 \right )} \sin{\left (3 x \right )} + \frac{3 \cdot 5^{\cos{\left (3 x \right )}}}{\sin{\left (3 x \right )}} \log{\left (5 \right )} \cos{\left (3 x \right )} + \frac{3 \cdot 5^{\cos{\left (3 x \right )}}}{\sin{\left (3 x \right )}} + \frac{6 \cdot 5^{\cos{\left (3 x \right )}}}{\sin^{3}{\left (3 x \right )}} \cos^{2}{\left (3 x \right )} - \frac{750 x^{7}}{\left(25 x^{6} + 1\right)^{2}} + \frac{10 x}{25 x^{6} + 1}\right)$$

Третья производная

  /                    6                                     12        cos(3*x)    3            cos(3*x)                                                cos(3*x)    2            \
  |    10        6750*x           cos(3*x)           225000*x      54*5        *cos (3*x)   45*5        *cos(3*x)      cos(3*x)    3       2        27*5        *cos (3*x)*log(5)|
3*|--------- - ------------ - 18*5        *log(5) + ------------ - ---------------------- - --------------------- - 9*5        *log (5)*sin (3*x) - -----------------------------|
  |        6              2                                    3            4                        2                                                           2               |
  |1 + 25*x    /        6\                          /        6\          sin (3*x)                sin (3*x)                                                   sin (3*x)          |
  \            \1 + 25*x /                          \1 + 25*x /                                                                                                                  /

$$3 \left(- 9 \cdot 5^{\cos{\left (3 x \right )}} \log^{3}{\left (5 \right )} \sin^{2}{\left (3 x \right )} - 18 \cdot 5^{\cos{\left (3 x \right )}} \log{\left (5 \right )} - \frac{27 \cdot 5^{\cos{\left (3 x \right )}}}{\sin^{2}{\left (3 x \right )}} \log{\left (5 \right )} \cos^{2}{\left (3 x \right )} - \frac{45 \cdot 5^{\cos{\left (3 x \right )}}}{\sin^{2}{\left (3 x \right )}} \cos{\left (3 x \right )} - \frac{54 \cdot 5^{\cos{\left (3 x \right )}}}{\sin^{4}{\left (3 x \right )}} \cos^{3}{\left (3 x \right )} + \frac{225000 x^{12}}{\left(25 x^{6} + 1\right)^{3}} - \frac{6750 x^{6}}{\left(25 x^{6} + 1\right)^{2}} + \frac{10}{25 x^{6} + 1}\right)$$