Производная 3^acos(2*x)

Вы ввели

 acos(2*x)
3         

$$3^{\operatorname{acos}{\left (2 x \right )}}$$

Первая производная

    acos(2*x)       
-2*3         *log(3)
--------------------
      __________    
     /        2     
   \/  1 - 4*x      

$$- \frac{2 \cdot 3^{\operatorname{acos}{\left (2 x \right )}}}{\sqrt{- 4 x^{2} + 1}} \log{\left (3 \right )}$$

Вторая производная

    acos(2*x) /  log(3)         2*x     \       
-4*3         *|--------- + -------------|*log(3)
              |        2             3/2|       
              |-1 + 4*x    /       2\   |       
              \            \1 - 4*x /   /       

$$- 4 \cdot 3^{\operatorname{acos}{\left (2 x \right )}} \left(\frac{2 x}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{\log{\left (3 \right )}}{4 x^{2} - 1}\right) \log{\left (3 \right )}$$

Третья производная

             /                        2                 2                   \       
   acos(2*x) |        1            log (3)          12*x         6*x*log(3) |       
8*3         *|- ------------- - ------------- - ------------- + ------------|*log(3)
             |            3/2             3/2             5/2              2|       
             |  /       2\      /       2\      /       2\      /        2\ |       
             \  \1 - 4*x /      \1 - 4*x /      \1 - 4*x /      \-1 + 4*x / /       

$$8 \cdot 3^{\operatorname{acos}{\left (2 x \right )}} \left(- \frac{12 x^{2}}{\left(- 4 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{6 x \log{\left (3 \right )}}{\left(4 x^{2} - 1\right)^{2}} - \frac{\log^{2}{\left (3 \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left (3 \right )}$$