Производная 2^asin(3*x)

Вы ввели

 asin(3*x)
2         

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

Первая производная

   asin(3*x)       
3*2         *log(2)
-------------------
      __________   
     /        2    
   \/  1 - 9*x     

$$\frac{3 \cdot 2^{\operatorname{asin}{\left (3 x \right )}}}{\sqrt{- 9 x^{2} + 1}} \log{\left (2 \right )}$$

Вторая производная

   asin(3*x) /    log(2)         3*x     \       
9*2         *|- --------- + -------------|*log(2)
             |          2             3/2|       
             |  -1 + 9*x    /       2\   |       
             \              \1 - 9*x /   /       

$$9 \cdot 2^{\operatorname{asin}{\left (3 x \right )}} \left(\frac{3 x}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{\log{\left (2 \right )}}{9 x^{2} - 1}\right) \log{\left (2 \right )}$$

Третья производная

              /                      2                 2                   \       
    asin(3*x) |      1            log (2)          27*x         9*x*log(2) |       
27*2         *|------------- + ------------- + ------------- + ------------|*log(2)
              |          3/2             3/2             5/2              2|       
              |/       2\      /       2\      /       2\      /        2\ |       
              \\1 - 9*x /      \1 - 9*x /      \1 - 9*x /      \-1 + 9*x / /       

$$27 \cdot 2^{\operatorname{asin}{\left (3 x \right )}} \left(\frac{27 x^{2}}{\left(- 9 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{9 x \log{\left (2 \right )}}{\left(9 x^{2} - 1\right)^{2}} + \frac{\log^{2}{\left (2 \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{1}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left (2 \right )}$$

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