Производная 2^asin(x)^(23)

Вы ввели

     23   
 asin  (x)
2         

$$2^{\operatorname{asin}^{23}{\left (x \right )}}$$

Первая производная

        23                    
    asin  (x)     22          
23*2         *asin  (x)*log(2)
------------------------------
            ________          
           /      2           
         \/  1 - x            

$$\frac{23 \cdot 2^{\operatorname{asin}^{23}{\left (x \right )}}}{\sqrt{- x^{2} + 1}} \log{\left (2 \right )} \operatorname{asin}^{22}{\left (x \right )}$$

Вторая производная

        23              /                                 23          \       
    asin  (x)     21    |     22      x*asin(x)    23*asin  (x)*log(2)|       
23*2         *asin  (x)*|- ------- + ----------- - -------------------|*log(2)
                        |        2           3/2               2      |       
                        |  -1 + x    /     2\            -1 + x       |       
                        \            \1 - x /                         /       

$$23 \cdot 2^{\operatorname{asin}^{23}{\left (x \right )}} \left(\frac{x \operatorname{asin}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{23 \operatorname{asin}^{23}{\left (x \right )}}{x^{2} - 1} \log{\left (2 \right )} - \frac{22}{x^{2} - 1}\right) \log{\left (2 \right )} \operatorname{asin}^{21}{\left (x \right )}$$

Третья производная

        23              /                    2          2     2                             46       2               23                      24          \       
    asin  (x)     20    |    462         asin (x)    3*x *asin (x)   66*x*asin(x)   529*asin  (x)*log (2)   1518*asin  (x)*log(2)   69*x*asin  (x)*log(2)|       
23*2         *asin  (x)*|----------- + ----------- + ------------- + ------------ + --------------------- + --------------------- + ---------------------|*log(2)
                        |        3/2           3/2            5/2              2                 3/2                     3/2                       2     |       
                        |/     2\      /     2\       /     2\        /      2\          /     2\                /     2\                 /      2\      |       
                        \\1 - x /      \1 - x /       \1 - x /        \-1 + x /          \1 - x /                \1 - x /                 \-1 + x /      /       

$$23 \cdot 2^{\operatorname{asin}^{23}{\left (x \right )}} \left(\frac{3 x^{2} \operatorname{asin}^{2}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{69 x \operatorname{asin}^{24}{\left (x \right )}}{\left(x^{2} - 1\right)^{2}} \log{\left (2 \right )} + \frac{66 x \operatorname{asin}{\left (x \right )}}{\left(x^{2} - 1\right)^{2}} + \frac{529 \operatorname{asin}^{46}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \log^{2}{\left (2 \right )} + \frac{1518 \operatorname{asin}^{23}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \log{\left (2 \right )} + \frac{\operatorname{asin}^{2}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{462}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left (2 \right )} \operatorname{asin}^{20}{\left (x \right )}$$