Производная 3^asin(x)/2

Вы ввели

 asin(x)
3       
--------
   2    

$$\frac{1}{2} 3^{\operatorname{asin}{\left (x \right )}}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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