Производная x*asin(log(x))

Вы ввели

x*asin(log(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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