Производная 2^asin(3/x)

Вы ввели

     /3\
 asin|-|
     \x/
2       

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

        /3\                                                                                                      
    asin|-| /                                                         2                                  \       
        \x/ |      2               21               81           3*log (2)       6*log(2)     27*log(2)  |       
-9*2       *|------------- + -------------- + -------------- + -------------- + ---------- + ------------|*log(2)
            |     ________              3/2              5/2              3/2     /    9 \              2|       
            |    /     9      2 /    9 \       4 /    9 \       2 /    9 \      x*|1 - --|    3 /    9 \ |       
            |   /  1 - --    x *|1 - --|      x *|1 - --|      x *|1 - --|        |     2|   x *|1 - --| |       
            |  /        2       |     2|         |     2|         |     2|        \    x /      |     2| |       
            \\/        x        \    x /         \    x /         \    x /                      \    x / /       
-----------------------------------------------------------------------------------------------------------------
                                                         4                                                       
                                                        x                                                        

$$- \frac{9}{x^{4}} 2^{\operatorname{asin}{\left (\frac{3}{x} \right )}} \left(\frac{2}{\sqrt{1 - \frac{9}{x^{2}}}} + \frac{6 \log{\left (2 \right )}}{x \left(1 - \frac{9}{x^{2}}\right)} + \frac{3 \log^{2}{\left (2 \right )}}{x^{2} \left(1 - \frac{9}{x^{2}}\right)^{\frac{3}{2}}} + \frac{21}{x^{2} \left(1 - \frac{9}{x^{2}}\right)^{\frac{3}{2}}} + \frac{27 \log{\left (2 \right )}}{x^{3} \left(1 - \frac{9}{x^{2}}\right)^{2}} + \frac{81}{x^{4} \left(1 - \frac{9}{x^{2}}\right)^{\frac{5}{2}}}\right) \log{\left (2 \right )}$$