Производная asin(log(5*x))

Вы ввели

asin(log(5*x))

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

Первая производная

         1          
--------------------
     _______________
    /        2      
x*\/  1 - log (5*x) 

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

Вторая производная

          log(5*x)   
  -1 + ------------- 
              2      
       1 - log (5*x) 
---------------------
      _______________
 2   /        2      
x *\/  1 - log (5*x) 

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

Третья производная

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

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