Производная (asin(log(x)))^2

Вы ввели

    2        
asin (log(x))

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

Первая производная

  2*asin(log(x))  
------------------
     _____________
    /        2    
x*\/  1 - log (x) 

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

Вторая производная

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

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

Третья производная

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

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