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The derivative of the function/ log(2*x-1)*acot(x)

Derivative of log(2*x-1)*acot(x)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
log(2*x - 1)*acot(x)
log⁡(2x−1)acot⁡(x)\log{\left(2 x - 1 \right)} \operatorname{acot}{\left(x \right)} 
log(2*x - 1)*acot(x)
The graph
02468-8-6-4-2-1010-250250
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  log(2*x - 1)   2*acot(x)
- ------------ + ---------
          2       2*x - 1 
     1 + x
−log⁡(2x−1)x2+1+2acot⁡(x)2x−1- \frac{\log{\left(2 x - 1 \right)}}{x^{2} + 1} + \frac{2 \operatorname{acot}{\left(x \right)}}{2 x - 1}
Simplify
The second derivative [src] 
  /           2             2*acot(x)    x*log(-1 + 2*x)\
2*|- ------------------- - ----------- + ---------------|
  |  /     2\                        2              2   |
  |  \1 + x /*(-1 + 2*x)   (-1 + 2*x)       /     2\    |
  \                                         \1 + x /    /
2(xlog⁡(2x−1)(x2+1)2−2(2x−1)(x2+1)−2acot⁡(x)(2x−1)2)2 \left(\frac{x \log{\left(2 x - 1 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2}{\left(2 x - 1\right) \left(x^{2} + 1\right)} - \frac{2 \operatorname{acot}{\left(x \right)}}{\left(2 x - 1\right)^{2}}\right)
Simplify
The third derivative [src] 
  /                                     /         2 \                                     \
  |                                     |      4*x  |                                     |
  |                                     |-1 + ------|*log(-1 + 2*x)                       |
  |                                     |          2|                                     |
  |         6              8*acot(x)    \     1 + x /                         6*x         |
2*|-------------------- + ----------- - --------------------------- + --------------------|
  |/     2\           2             3                    2                    2           |
  |\1 + x /*(-1 + 2*x)    (-1 + 2*x)             /     2\             /     2\            |
  \                                              \1 + x /             \1 + x / *(-1 + 2*x)/
2(6x(2x−1)(x2+1)2−(4x2x2+1−1)log⁡(2x−1)(x2+1)2+6(2x−1)2(x2+1)+8acot⁡(x)(2x−1)3)2 \left(\frac{6 x}{\left(2 x - 1\right) \left(x^{2} + 1\right)^{2}} - \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(2 x - 1 \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6}{\left(2 x - 1\right)^{2} \left(x^{2} + 1\right)} + \frac{8 \operatorname{acot}{\left(x \right)}}{\left(2 x - 1\right)^{3}}\right)
Simplify
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