Производная coth(4*x)^5*acos(2*x)

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Решение

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    5               
coth (4*x)*acos(2*x)
$$\coth^{5}{\left (4 x \right )} \operatorname{acos}{\left (2 x \right )}$$
График
Первая производная
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         5               4               
   2*coth (4*x)   20*coth (4*x)*acos(2*x)
- ------------- - -----------------------
     __________              2           
    /        2           sinh (4*x)      
  \/  1 - 4*x                            
$$- \frac{20 \coth^{4}{\left (4 x \right )}}{\sinh^{2}{\left (4 x \right )}} \operatorname{acos}{\left (2 x \right )} - \frac{2 \coth^{5}{\left (4 x \right )}}{\sqrt{- 4 x^{2} + 1}}$$
Вторая производная
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             /                      2                                                                   \
      3      |40*acos(2*x)    x*coth (4*x)         10*coth(4*x)         20*acos(2*x)*cosh(4*x)*coth(4*x)|
8*coth (4*x)*|------------ - ------------- + ------------------------ + --------------------------------|
             |     4                   3/2      __________                             3                |
             | sinh (4*x)    /       2\        /        2      2                   sinh (4*x)           |
             \               \1 - 4*x /      \/  1 - 4*x  *sinh (4*x)                                   /
$$8 \left(- \frac{x \coth^{2}{\left (4 x \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{20 \operatorname{acos}{\left (2 x \right )}}{\sinh^{3}{\left (4 x \right )}} \cosh{\left (4 x \right )} \coth{\left (4 x \right )} + \frac{40 \operatorname{acos}{\left (2 x \right )}}{\sinh^{4}{\left (4 x \right )}} + \frac{10 \coth{\left (4 x \right )}}{\sqrt{- 4 x^{2} + 1} \sinh^{2}{\left (4 x \right )}}\right) \coth^{3}{\left (4 x \right )}$$
Третья производная
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             /        3                                                        2     3               2                                                              2          2                          2                               2          \
      2      |    coth (4*x)    480*acos(2*x)        240*coth(4*x)         12*x *coth (4*x)   80*coth (4*x)*acos(2*x)   960*acos(2*x)*cosh(4*x)*coth(4*x)   240*cosh (4*x)*coth (4*x)*acos(2*x)   120*coth (4*x)*cosh(4*x)       60*x*coth (4*x)     |
8*coth (4*x)*|- ------------- - ------------- - ------------------------ - ---------------- + ----------------------- - --------------------------------- - ----------------------------------- - ------------------------ + ------------------------|
             |            3/2         6            __________                         5/2                2                              5                                    4                       __________                        3/2           |
             |  /       2\        sinh (4*x)      /        2      4         /       2\               sinh (4*x)                     sinh (4*x)                           sinh (4*x)                 /        2      3        /       2\        2     |
             \  \1 - 4*x /                      \/  1 - 4*x  *sinh (4*x)    \1 - 4*x /                                                                                                            \/  1 - 4*x  *sinh (4*x)   \1 - 4*x /   *sinh (4*x)/
$$8 \left(- \frac{12 x^{2} \coth^{3}{\left (4 x \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{60 x \coth^{2}{\left (4 x \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}} \sinh^{2}{\left (4 x \right )}} + \frac{80 \coth^{2}{\left (4 x \right )}}{\sinh^{2}{\left (4 x \right )}} \operatorname{acos}{\left (2 x \right )} - \frac{240 \cosh^{2}{\left (4 x \right )}}{\sinh^{4}{\left (4 x \right )}} \coth^{2}{\left (4 x \right )} \operatorname{acos}{\left (2 x \right )} - \frac{960 \operatorname{acos}{\left (2 x \right )}}{\sinh^{5}{\left (4 x \right )}} \cosh{\left (4 x \right )} \coth{\left (4 x \right )} - \frac{480 \operatorname{acos}{\left (2 x \right )}}{\sinh^{6}{\left (4 x \right )}} - \frac{120 \cosh{\left (4 x \right )} \coth^{2}{\left (4 x \right )}}{\sqrt{- 4 x^{2} + 1} \sinh^{3}{\left (4 x \right )}} - \frac{240 \coth{\left (4 x \right )}}{\sqrt{- 4 x^{2} + 1} \sinh^{4}{\left (4 x \right )}} - \frac{\coth^{3}{\left (4 x \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}}\right) \coth^{2}{\left (4 x \right )}$$