Производная acos(log(2*x))

Вы ввели

acos(log(2*x))

$$\operatorname{acos}{\left(\log{\left(2 x \right)} \right)}$$

d                 
--(acos(log(2*x)))
dx                

$$\frac{d}{d x} \operatorname{acos}{\left(\log{\left(2 x \right)} \right)}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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

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