Производная acos(log(x))

Вы ввели

acos(log(x))

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

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

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