Производная acos(3*x)^4

Вы ввели

    4     
acos (3*x)

$$\operatorname{acos}^{4}{\left (3 x \right )}$$

Первая производная

        3     
-12*acos (3*x)
--------------
   __________ 
  /        2  
\/  1 - 9*x   

$$- \frac{12 \operatorname{acos}^{3}{\left (3 x \right )}}{\sqrt{- 9 x^{2} + 1}}$$

Вторая производная

         2      /    1        x*acos(3*x) \
-108*acos (3*x)*|--------- + -------------|
                |        2             3/2|
                |-1 + 9*x    /       2\   |
                \            \1 - 9*x /   /

$$- 108 \left(\frac{x \operatorname{acos}{\left (3 x \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{1}{9 x^{2} - 1}\right) \operatorname{acos}^{2}{\left (3 x \right )}$$

Третья производная

    /                        2             2     2                      \          
    |        6           acos (3*x)    27*x *acos (3*x)   27*x*acos(3*x)|          
108*|- ------------- - ------------- - ---------------- + --------------|*acos(3*x)
    |            3/2             3/2              5/2                 2 |          
    |  /       2\      /       2\       /       2\         /        2\  |          
    \  \1 - 9*x /      \1 - 9*x /       \1 - 9*x /         \-1 + 9*x /  /          

$$108 \left(- \frac{27 x^{2} \operatorname{acos}^{2}{\left (3 x \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{27 x \operatorname{acos}{\left (3 x \right )}}{\left(9 x^{2} - 1\right)^{2}} - \frac{\operatorname{acos}^{2}{\left (3 x \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{6}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{acos}{\left (3 x \right )}$$