Производная acos(log(3*x))

Вы ввели

acos(log(3*x))

$$\operatorname{acos}{\left (\log{\left (3 x \right )} \right )}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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