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y=(x*arctgx)/(1+x^(2))
Derivada de la función/ arctg/ x^(2)/ y=(x*arctgx)/(1+x^(2))

Derivada de y=(x*arctgx)/(1+x^(2))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
x*acot(x)
---------
       2 
  1 + x
xacot⁡(x)x2+1\frac{x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} 
(x*acot(x))/(1 + x^2)
Gráfica
02468-8-6-4-2-10102.5-2.5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    x                            
- ------ + acot(x)               
       2                2        
  1 + x              2*x *acot(x)
------------------ - ------------
           2                  2  
      1 + x           /     2\   
                      \1 + x /
−2x2acot⁡(x)(x2+1)2+−xx2+1+acot⁡(x)x2+1- \frac{2 x^{2} \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{- \frac{x}{x^{2} + 1} + \operatorname{acot}{\left(x \right)}}{x^{2} + 1}
Simplificar
Segunda derivada [src] 
  /        2                                 /         2 \        \
  |       x          /             x   \     |      4*x  |        |
2*|-1 + ------ + 2*x*|-acot(x) + ------| + x*|-1 + ------|*acot(x)|
  |          2       |                2|     |          2|        |
  \     1 + x        \           1 + x /     \     1 + x /        /
-------------------------------------------------------------------
                                     2                             
                             /     2\                              
                             \1 + x /
2(x2x2+1+2x(xx2+1−acot⁡(x))+x(4x2x2+1−1)acot⁡(x)−1)(x2+1)2\frac{2 \left(\frac{x^{2}}{x^{2} + 1} + 2 x \left(\frac{x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right) + x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{acot}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}}
Simplificar
Tercera derivada [src] 
   /                                           /        2  \         /         2 \        \
   |                                           |       x   |       2 |      2*x  |        |
   |                                      10*x*|-1 + ------|   12*x *|-1 + ------|*acot(x)|
   |  /         2 \                            |          2|         |          2|        |
   |  |      4*x  | /             x   \        \     1 + x /         \     1 + x /        |
-2*|3*|-1 + ------|*|-acot(x) + ------| + ------------------ + ---------------------------|
   |  |          2| |                2|              2                         2          |
   \  \     1 + x / \           1 + x /         1 + x                     1 + x           /
-------------------------------------------------------------------------------------------
                                                 2                                         
                                         /     2\                                          
                                         \1 + x /
−2(12x2(2x2x2+1−1)acot⁡(x)x2+1+10x(x2x2+1−1)x2+1+3(xx2+1−acot⁡(x))(4x2x2+1−1))(x2+1)2- \frac{2 \left(\frac{12 x^{2} \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{10 x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + 3 \left(\frac{x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)\right)}{\left(x^{2} + 1\right)^{2}}
Simplificar
Gráfico
Derivada de y=(x*arctgx)/(1+x^(2))
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