Производная 5^asin(x)^2

Вы ввели

     2   
 asin (x)
5        

$$5^{\operatorname{asin}^{2}{\left(x \right)}}$$

  /     2   \
d | asin (x)|
--\5        /
dx           

$$\frac{d}{d x} 5^{\operatorname{asin}^{2}{\left(x \right)}}$$

Первая производная

       2                  
   asin (x)               
2*5        *asin(x)*log(5)
--------------------------
          ________        
         /      2         
       \/  1 - x          

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

Вторая производная

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

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

Третья производная

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

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

График