Производная acos(log(x)^(2))

Вы ввели

    /   2   \
acos\log (x)/

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

Первая производная

    -2*log(x)     
------------------
     _____________
    /        4    
x*\/  1 - log (x) 

$$- \frac{2 \log{\left (x \right )}}{x \sqrt{- \log^{4}{\left (x \right )} + 1}}$$

Вторая производная

  /           4             \
  |      2*log (x)          |
2*|-1 - ----------- + log(x)|
  |            4            |
  \     1 - log (x)         /
-----------------------------
           _____________     
      2   /        4         
     x *\/  1 - log (x)      

$$\frac{1}{x^{2} \sqrt{- \log^{4}{\left (x \right )} + 1}} \left(2 \log{\left (x \right )} - 2 - \frac{4 \log^{4}{\left (x \right )}}{- \log^{4}{\left (x \right )} + 1}\right)$$

Третья производная

  /                       7               3            4    \
  |                 12*log (x)      10*log (x)    6*log (x) |
2*|3 - 2*log(x) - -------------- - ----------- + -----------|
  |                            2          4             4   |
  |               /       4   \    1 - log (x)   1 - log (x)|
  \               \1 - log (x)/                             /
-------------------------------------------------------------
                           _____________                     
                      3   /        4                         
                     x *\/  1 - log (x)                      

$$\frac{1}{x^{3} \sqrt{- \log^{4}{\left (x \right )} + 1}} \left(- 4 \log{\left (x \right )} + 6 + \frac{12 \log^{4}{\left (x \right )}}{- \log^{4}{\left (x \right )} + 1} - \frac{20 \log^{3}{\left (x \right )}}{- \log^{4}{\left (x \right )} + 1} - \frac{24 \log^{7}{\left (x \right )}}{\left(- \log^{4}{\left (x \right )} + 1\right)^{2}}\right)$$