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Derivative of:
Derivative of 3*x-1
Derivative of x*sin(2*x)
Derivative of (x^4+5)^cot(x)
Derivative of (x-3)*sqrt(x)
Identical expressions
cth4x^ five *arccos2x
cth4x to the power of 5 multiply by arc co sinus of e of 2x
cth4x to the power of five multiply by arc co sinus of e of 2x
cth4x5*arccos2x
cth4x⁵*arccos2x
cth4x^5arccos2x
cth4x5arccos2x

The derivative of the function/ cth4x^5*arccos2x

Derivative of cth4x^5*arccos2x

The solution

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    5               
coth (4*x)*acos(2*x)

\coth^{5}{\left(4 x \right)} \operatorname{acos}{\left(2 x \right)}

d /    5               \
--\coth (4*x)*acos(2*x)/
dx

\frac{d}{d x} \coth^{5}{\left(4 x \right)} \operatorname{acos}{\left(2 x \right)}

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The first derivative [src]

         5               4               
   2*coth (4*x)   20*coth (4*x)*acos(2*x)
- ------------- - -----------------------
     __________              2           
    /        2           sinh (4*x)      
  \/  1 - 4*x

- \frac{2 \coth^{5}{\left(4 x \right)}}{\sqrt{- 4 x^{2} + 1}} - \frac{20 \coth^{4}{\left(4 x \right)} \operatorname{acos}{\left(2 x \right)}}{\sinh^{2}{\left(4 x \right)}}

Simplify

The second derivative [src]

             /                                                /    2                          \          \
             |         2                                   20*|--------- + cosh(4*x)*coth(4*x)|*acos(2*x)|
      3      |   x*coth (4*x)         10*coth(4*x)            \sinh(4*x)                      /          |
8*coth (4*x)*|- ------------- + ------------------------ + ----------------------------------------------|
             |            3/2      __________                                    3                       |
             |  /       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 \left(\cosh{\left(4 x \right)} \coth{\left(4 x \right)} + \frac{2}{\sinh{\left(4 x \right)}}\right) \operatorname{acos}{\left(2 x \right)}}{\sinh^{3}{\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)}

Simplify

The third derivative [src]

             /           /           2  \      /                                  2          2                              \                                                                                       \
             |    3      |       12*x   |      |      2            6        3*cosh (4*x)*coth (4*x)   12*cosh(4*x)*coth(4*x)|                                                                                       |
             |coth (4*x)*|-1 + ---------|   80*|- coth (4*x) + ---------- + ----------------------- + ----------------------|*acos(2*x)       /    2                          \                                     |
             |           |             2|      |                   4                   2                        3           |             120*|--------- + cosh(4*x)*coth(4*x)|*coth(4*x)                2          |
      2      |           \     -1 + 4*x /      \               sinh (4*x)          sinh (4*x)               sinh (4*x)      /                 \sinh(4*x)                      /                 60*x*coth (4*x)     |
8*coth (4*x)*|--------------------------- - ------------------------------------------------------------------------------------------- - ----------------------------------------------- + ------------------------|
             |                 3/2                                                       2                                                               __________                                   3/2           |
             |       /       2\                                                      sinh (4*x)                                                         /        2      3                   /       2\        2     |
             \       \1 - 4*x /                                                                                                                       \/  1 - 4*x  *sinh (4*x)              \1 - 4*x /   *sinh (4*x)/

8 \cdot \left(\frac{\left(\frac{12 x^{2}}{4 x^{2} - 1} - 1\right) \coth^{3}{\left(4 x \right)}}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{80 \left(- \coth^{2}{\left(4 x \right)} + \frac{3 \cosh^{2}{\left(4 x \right)} \coth^{2}{\left(4 x \right)}}{\sinh^{2}{\left(4 x \right)}} + \frac{12 \cosh{\left(4 x \right)} \coth{\left(4 x \right)}}{\sinh^{3}{\left(4 x \right)}} + \frac{6}{\sinh^{4}{\left(4 x \right)}}\right) \operatorname{acos}{\left(2 x \right)}}{\sinh^{2}{\left(4 x \right)}} + \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{120 \left(\cosh{\left(4 x \right)} \coth{\left(4 x \right)} + \frac{2}{\sinh{\left(4 x \right)}}\right) \coth{\left(4 x \right)}}{\sqrt{- 4 x^{2} + 1} \sinh^{3}{\left(4 x \right)}}\right) \coth^{2}{\left(4 x \right)}

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Derivative of cth4x^5*arccos2x

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