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y=arctg(x+1/x-1)
Derivada de la función/ x+1/x/ arctg/ 1/x-1/ y=arctg(x+1/x-1)

Derivada de y=arctg(x+1/x-1)

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    /    1    \
atan|x + - - 1|
    \    x    /
atan⁡((x+1x)−1)\operatorname{atan}{\left(\left(x + \frac{1}{x}\right) - 1 \right)} 
atan(x + 1/x - 1)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         1      
     1 - --     
          2     
         x      
----------------
               2
    /    1    \ 
1 + |x + - - 1| 
    \    x    /
1−1x2((x+1x)−1)2+1\frac{1 - \frac{1}{x^{2}}}{\left(\left(x + \frac{1}{x}\right) - 1\right)^{2} + 1}
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Segunda derivada [src] 
  /             2             \
  |     /    1 \  /         1\|
  |     |1 - --| *|-1 + x + -||
  |     |     2|  \         x/|
  |1    \    x /              |
2*|-- - ----------------------|
  | 3                     2   |
  |x          /         1\    |
  |       1 + |-1 + x + -|    |
  \           \         x/    /
-------------------------------
                       2       
           /         1\        
       1 + |-1 + x + -|        
           \         x/
2(−(1−1x2)2(x−1+1x)(x−1+1x)2+1+1x3)(x−1+1x)2+1\frac{2 \left(- \frac{\left(1 - \frac{1}{x^{2}}\right)^{2} \left(x - 1 + \frac{1}{x}\right)}{\left(x - 1 + \frac{1}{x}\right)^{2} + 1} + \frac{1}{x^{3}}\right)}{\left(x - 1 + \frac{1}{x}\right)^{2} + 1}
Simplificar
Tercera derivada [src] 
  /                   3                 3             2                          \
  |           /    1 \          /    1 \  /         1\      /    1 \ /         1\|
  |           |1 - --|        4*|1 - --| *|-1 + x + -|    6*|1 - --|*|-1 + x + -||
  |           |     2|          |     2|  \         x/      |     2| \         x/|
  |  3        \    x /          \    x /                    \    x /             |
2*|- -- - ----------------- + ------------------------- - -----------------------|
  |   4                   2                         2         /                2\|
  |  x        /         1\       /                2\        3 |    /         1\ ||
  |       1 + |-1 + x + -|       |    /         1\ |       x *|1 + |-1 + x + -| ||
  |           \         x/       |1 + |-1 + x + -| |          \    \         x/ /|
  \                              \    \         x/ /                             /
----------------------------------------------------------------------------------
                                                2                                 
                                    /         1\                                  
                                1 + |-1 + x + -|                                  
                                    \         x/
2(−(1−1x2)3(x−1+1x)2+1+4(1−1x2)3(x−1+1x)2((x−1+1x)2+1)2−6(1−1x2)(x−1+1x)x3((x−1+1x)2+1)−3x4)(x−1+1x)2+1\frac{2 \left(- \frac{\left(1 - \frac{1}{x^{2}}\right)^{3}}{\left(x - 1 + \frac{1}{x}\right)^{2} + 1} + \frac{4 \left(1 - \frac{1}{x^{2}}\right)^{3} \left(x - 1 + \frac{1}{x}\right)^{2}}{\left(\left(x - 1 + \frac{1}{x}\right)^{2} + 1\right)^{2}} - \frac{6 \left(1 - \frac{1}{x^{2}}\right) \left(x - 1 + \frac{1}{x}\right)}{x^{3} \left(\left(x - 1 + \frac{1}{x}\right)^{2} + 1\right)} - \frac{3}{x^{4}}\right)}{\left(x - 1 + \frac{1}{x}\right)^{2} + 1}
Simplificar
Gráfico
Derivada de y=arctg(x+1/x-1)
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