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The derivative of the function/ (arctgx+1)/x

Derivative of (arctgx+1)/x

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

The graph:

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The solution

You have entered [src] 
acot(x) + 1
-----------
     x
$$\frac{\operatorname{acot}{\left(x \right)} + 1}{x}$$ 
(acot(x) + 1)/x
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      1        acot(x) + 1
- ---------- - -----------
    /     2\         2    
  x*\1 + x /        x
$$- \frac{1}{x \left(x^{2} + 1\right)} - \frac{\operatorname{acot}{\left(x \right)} + 1}{x^{2}}$$
Simplify
The second derivative [src] 
  /    1       1 + acot(x)        1     \
2*|--------- + ----------- + -----------|
  |        2         3        2 /     2\|
  |/     2\         x        x *\1 + x /|
  \\1 + x /                             /
$$2 \left(\frac{1}{\left(x^{2} + 1\right)^{2}} + \frac{1}{x^{2} \left(x^{2} + 1\right)} + \frac{\operatorname{acot}{\left(x \right)} + 1}{x^{3}}\right)$$
Simplify
The third derivative [src] 
   /                     2                                 \
   |                  4*x                                  |
   |            -1 + ------                                |
   |                      2                                |
   |    3            1 + x    3*(1 + acot(x))        3     |
-2*|--------- + ----------- + --------------- + -----------|
   |        2            2            3          2 /     2\|
   |/     2\     /     2\            x          x *\1 + x /|
   \\1 + x /     \1 + x /                                  /
------------------------------------------------------------
                             x
$$- \frac{2 \left(\frac{\frac{4 x^{2}}{x^{2} + 1} - 1}{\left(x^{2} + 1\right)^{2}} + \frac{3}{\left(x^{2} + 1\right)^{2}} + \frac{3}{x^{2} \left(x^{2} + 1\right)} + \frac{3 \left(\operatorname{acot}{\left(x \right)} + 1\right)}{x^{3}}\right)}{x}$$
Simplify
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