Производная (acos(5*log(x)))

Вы ввели

acos(5*log(x))

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

Первая производная

         -5          
---------------------
     ________________
    /           2    
x*\/  1 - 25*log (x) 

$$- \frac{5}{x \sqrt{- 25 \log^{2}{\left (x \right )} + 1}}$$

Вторая производная

  /      25*log(x)   \
5*|1 - --------------|
  |              2   |
  \    1 - 25*log (x)/
----------------------
      ________________
 2   /           2    
x *\/  1 - 25*log (x) 

$$\frac{5 - \frac{125 \log{\left (x \right )}}{- 25 \log^{2}{\left (x \right )} + 1}}{x^{2} \sqrt{- 25 \log^{2}{\left (x \right )} + 1}}$$

Третья производная

  /                                 2                      \
  |           25            1875*log (x)       75*log(x)   |
5*|-2 - -------------- - ----------------- + --------------|
  |               2                      2             2   |
  |     1 - 25*log (x)   /          2   \    1 - 25*log (x)|
  \                      \1 - 25*log (x)/                  /
------------------------------------------------------------
                         ________________                   
                    3   /           2                       
                   x *\/  1 - 25*log (x)                    

$$\frac{1}{x^{3} \sqrt{- 25 \log^{2}{\left (x \right )} + 1}} \left(-10 + \frac{375 \log{\left (x \right )}}{- 25 \log^{2}{\left (x \right )} + 1} - \frac{125}{- 25 \log^{2}{\left (x \right )} + 1} - \frac{9375 \log^{2}{\left (x \right )}}{\left(- 25 \log^{2}{\left (x \right )} + 1\right)^{2}}\right)$$