Производная (acos(3*x))/x^(1/7)

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Решение

Вы ввели
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[text]
acos(3*x)
---------
  7 ___  
  \/ x   
$$\frac{1}{\sqrt[7]{x}} \operatorname{acos}{\left (3 x \right )}$$
График
Первая производная
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           3            acos(3*x)
- ------------------- - ---------
           __________        8/7 
  7 ___   /        2      7*x    
  \/ x *\/  1 - 9*x              
$$- \frac{3}{\sqrt[7]{x} \sqrt{- 9 x^{2} + 1}} - \frac{1}{7 x^{\frac{8}{7}}} \operatorname{acos}{\left (3 x \right )}$$
Вторая производная
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         6/7                                        
     27*x                  6             8*acos(3*x)
- ------------- + -------------------- + -----------
            3/2             __________         15/7 
  /       2\         8/7   /        2      49*x     
  \1 - 9*x /      7*x   *\/  1 - 9*x                
$$- \frac{27 x^{\frac{6}{7}}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{7 x^{\frac{8}{7}} \sqrt{- 9 x^{2} + 1}} + \frac{8}{49 x^{\frac{15}{7}}} \operatorname{acos}{\left (3 x \right )}$$
Третья производная
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   /       13/7                                                                  \
   |  243*x                   24                       36            40*acos(3*x)|
-3*|------------- + ---------------------- + --------------------- + ------------|
   |          5/2               __________                     3/2         22/7  |
   |/       2\          15/7   /        2      7 ___ /       2\       343*x      |
   \\1 - 9*x /      49*x    *\/  1 - 9*x     7*\/ x *\1 - 9*x /                  /
$$- 3 \left(\frac{243 x^{\frac{13}{7}}}{\left(- 9 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{36}{7 \sqrt[7]{x} \left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{24}{49 x^{\frac{15}{7}} \sqrt{- 9 x^{2} + 1}} + \frac{40}{343 x^{\frac{22}{7}}} \operatorname{acos}{\left (3 x \right )}\right)$$