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The derivative of the function/ arcctg(2*x)*arctg(2*x)

Derivative of arcctg(2*x)*arctg(2*x)

Function f() - derivative -N order at the point
v

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Piecewise:

The solution

You have entered [src] 
acot(2*x)*atan(2*x)
$$\operatorname{acot}{\left(2 x \right)} \operatorname{atan}{\left(2 x \right)}$$ 
acot(2*x)*atan(2*x)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  2*atan(2*x)   2*acot(2*x)
- ----------- + -----------
           2             2 
    1 + 4*x       1 + 4*x
$$\frac{2 \operatorname{acot}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{2 \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}$$
Simplify
The second derivative [src] 
8*(-1 - 2*x*acot(2*x) + 2*x*atan(2*x))
--------------------------------------
                       2              
             /       2\               
             \1 + 4*x /
$$\frac{8 \left(- 2 x \operatorname{acot}{\left(2 x \right)} + 2 x \operatorname{atan}{\left(2 x \right)} - 1\right)}{\left(4 x^{2} + 1\right)^{2}}$$
Simplify
The third derivative [src] 
   //          2  \             /          2  \                     \
   ||      16*x   |             |      16*x   |               12*x  |
16*||-1 + --------|*acot(2*x) - |-1 + --------|*atan(2*x) + --------|
   ||            2|             |            2|                    2|
   \\     1 + 4*x /             \     1 + 4*x /             1 + 4*x /
---------------------------------------------------------------------
                                       2                             
                             /       2\                              
                             \1 + 4*x /
$$\frac{16 \left(\frac{12 x}{4 x^{2} + 1} + \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right) \operatorname{acot}{\left(2 x \right)} - \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right) \operatorname{atan}{\left(2 x \right)}\right)}{\left(4 x^{2} + 1\right)^{2}}$$
Simplify
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