Производная acos(x^(1/2))/(tan(2*x^5))^(1/4)

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Решение

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     /  ___\  
 acos\\/ x /  
--------------
   ___________
4 /    /   5\ 
\/  tan\2*x / 
$$\frac{\operatorname{acos}{\left (\sqrt{x} \right )}}{\sqrt[4]{\tan{\left (2 x^{5} \right )}}}$$
График
Первая производная
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                                        4 /       2/   5\\     /  ___\
                 1                   5*x *\1 + tan \2*x //*acos\\/ x /
- -------------------------------- - ---------------------------------
                       ___________                  5/4/   5\         
      ___   _______ 4 /    /   5\              2*tan   \2*x /         
  2*\/ x *\/ 1 - x *\/  tan\2*x /                                     
$$- \frac{5 x^{4} \operatorname{acos}{\left (\sqrt{x} \right )}}{2 \tan^{\frac{5}{4}}{\left (2 x^{5} \right )}} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right) - \frac{1}{2 \sqrt{x} \sqrt{- x + 1} \sqrt[4]{\tan{\left (2 x^{5} \right )}}}$$
Вторая производная
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                                                                                                                                                                     2            
                                                                                   3 /       2/   5\\     /  ___\      7/2 /       2/   5\\        8 /       2/   5\\      /  ___\
          1                   1               8 /       2/   5\\     /  ___\   10*x *\1 + tan \2*x //*acos\\/ x /   5*x   *\1 + tan \2*x //   125*x *\1 + tan \2*x // *acos\\/ x /
- ------------------ + ---------------- - 50*x *\1 + tan \2*x //*acos\\/ x / - ---------------------------------- + ----------------------- + ------------------------------------
      ___        3/2      3/2   _______                                                       /   5\                     _______    /   5\                     2/   5\            
  4*\/ x *(1 - x)      4*x   *\/ 1 - x                                                     tan\2*x /                 2*\/ 1 - x *tan\2*x /                4*tan \2*x /            
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                                                                                     ___________                                                                                  
                                                                                  4 /    /   5\                                                                                   
                                                                                  \/  tan\2*x /                                                                                   
$$\frac{1}{\sqrt[4]{\tan{\left (2 x^{5} \right )}}} \left(\frac{5 x^{\frac{7}{2}} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right)}{2 \sqrt{- x + 1} \tan{\left (2 x^{5} \right )}} + \frac{125 x^{8} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right)^{2}}{4 \tan^{2}{\left (2 x^{5} \right )}} \operatorname{acos}{\left (\sqrt{x} \right )} - 50 x^{8} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right) \operatorname{acos}{\left (\sqrt{x} \right )} - \frac{10 x^{3} \operatorname{acos}{\left (\sqrt{x} \right )}}{\tan{\left (2 x^{5} \right )}} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right) - \frac{1}{4 \sqrt{x} \left(- x + 1\right)^{\frac{3}{2}}} + \frac{1}{4 x^{\frac{3}{2}} \sqrt{- x + 1}}\right)$$
Третья производная
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                                                                                                                                                                                                                                                                                              2                                        2                                        3                                         2                                                        
                                                                                                                                                                     7 /       2/   5\\     /  ___\       2 /       2/   5\\     /  ___\       15/2 /       2/   5\\        7 /       2/   5\\      /  ___\         12 /       2/   5\\      /  ___\         12 /       2/   5\\      /  ___\        15/2 /       2/   5\\         7/2 /       2/   5\\        5/2 /       2/   5\\
                 3                                  3                                  1                         12    3/4/   5\ /       2/   5\\     /  ___\   600*x *\1 + tan \2*x //*acos\\/ x /   30*x *\1 + tan \2*x //*acos\\/ x /   75*x    *\1 + tan \2*x //   375*x *\1 + tan \2*x // *acos\\/ x /   1375*x  *\1 + tan \2*x // *acos\\/ x /   5625*x  *\1 + tan \2*x // *acos\\/ x /   375*x    *\1 + tan \2*x //     15*x   *\1 + tan \2*x //   105*x   *\1 + tan \2*x //
- ------------------------------- - --------------------------------- + -------------------------------- - 1000*x  *tan   \2*x /*\1 + tan \2*x //*acos\\/ x / - ----------------------------------- - ---------------------------------- + ------------------------- + ------------------------------------ + -------------------------------------- - -------------------------------------- - --------------------------- + ------------------------- + -------------------------
                      ___________                         ___________                        ___________                                                                      ___________                           5/4/   5\                            ___________                  9/4/   5\                               5/4/   5\                                13/4/   5\                     _______    9/4/   5\             3/2    5/4/   5\        _______    5/4/   5\
     5/2   _______ 4 /    /   5\        ___        5/2 4 /    /   5\       3/2        3/2 4 /    /   5\                                                                    4 /    /   5\                         tan   \2*x /                 _______ 4 /    /   5\                tan   \2*x /                            tan   \2*x /                           8*tan    \2*x /                 8*\/ 1 - x *tan   \2*x /    8*(1 - x)   *tan   \2*x /    8*\/ 1 - x *tan   \2*x /
  8*x   *\/ 1 - x *\/  tan\2*x /    8*\/ x *(1 - x)   *\/  tan\2*x /    4*x   *(1 - x)   *\/  tan\2*x /                                                                    \/  tan\2*x /                                                    \/ 1 - x *\/  tan\2*x /                                                                                                                                                                                                                
$$- \frac{375 x^{\frac{15}{2}} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right)^{2}}{8 \sqrt{- x + 1} \tan^{\frac{9}{4}}{\left (2 x^{5} \right )}} + \frac{75 x^{\frac{15}{2}} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right)}{\sqrt{- x + 1} \sqrt[4]{\tan{\left (2 x^{5} \right )}}} + \frac{15 x^{\frac{7}{2}} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right)}{8 \left(- x + 1\right)^{\frac{3}{2}} \tan^{\frac{5}{4}}{\left (2 x^{5} \right )}} + \frac{105 x^{\frac{5}{2}} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right)}{8 \sqrt{- x + 1} \tan^{\frac{5}{4}}{\left (2 x^{5} \right )}} - \frac{5625 x^{12} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right)^{3}}{8 \tan^{\frac{13}{4}}{\left (2 x^{5} \right )}} \operatorname{acos}{\left (\sqrt{x} \right )} + \frac{1375 x^{12} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right)^{2}}{\tan^{\frac{5}{4}}{\left (2 x^{5} \right )}} \operatorname{acos}{\left (\sqrt{x} \right )} - 1000 x^{12} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right) \tan^{\frac{3}{4}}{\left (2 x^{5} \right )} \operatorname{acos}{\left (\sqrt{x} \right )} + \frac{375 x^{7} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right)^{2}}{\tan^{\frac{9}{4}}{\left (2 x^{5} \right )}} \operatorname{acos}{\left (\sqrt{x} \right )} - \frac{600 x^{7} \operatorname{acos}{\left (\sqrt{x} \right )}}{\sqrt[4]{\tan{\left (2 x^{5} \right )}}} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right) - \frac{30 x^{2} \operatorname{acos}{\left (\sqrt{x} \right )}}{\tan^{\frac{5}{4}}{\left (2 x^{5} \right )}} \left(\tan^{2}{\left (2 x^{5} \right )} + 1\right) - \frac{3}{8 \sqrt{x} \left(- x + 1\right)^{\frac{5}{2}} \sqrt[4]{\tan{\left (2 x^{5} \right )}}} + \frac{1}{4 x^{\frac{3}{2}} \left(- x + 1\right)^{\frac{3}{2}} \sqrt[4]{\tan{\left (2 x^{5} \right )}}} - \frac{3}{8 x^{\frac{5}{2}} \sqrt{- x + 1} \sqrt[4]{\tan{\left (2 x^{5} \right )}}}$$