Mister Exam

Other calculators

The derivative of the function/ arctgx+1/x-1

Derivative of arctgx+1/x-1

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

The graph:

from to

Piecewise:

The solution

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