Производная asin(log(x))

Вы ввели

asin(log(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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