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

Derivada de y=(xarctgx)/(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*atan(x)
---------
       2 
  1 + x
xatan⁡(x)x2+1\frac{x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} 
(x*atan(x))/(1 + x^2)
Gráfica
02468-8-6-4-2-10101-1
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  x                            
------ + atan(x)               
     2                2        
1 + x              2*x *atan(x)
---------------- - ------------
          2                 2  
     1 + x          /     2\   
                    \1 + x /
−2x2atan⁡(x)(x2+1)2+xx2+1+atan⁡(x)x2+1- \frac{2 x^{2} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}}{x^{2} + 1}
Simplificar
Segunda derivada [src] 
  /       2                                /         2 \        \
  |      x          /  x             \     |      4*x  |        |
2*|1 - ------ - 2*x*|------ + atan(x)| + x*|-1 + ------|*atan(x)|
  |         2       |     2          |     |          2|        |
  \    1 + x        \1 + x           /     \     1 + x /        /
-----------------------------------------------------------------
                                    2                            
                            /     2\                             
                            \1 + x /
2(−x2x2+1−2x(xx2+1+atan⁡(x))+x(4x2x2+1−1)atan⁡(x)+1)(x2+1)2\frac{2 \left(- \frac{x^{2}}{x^{2} + 1} - 2 x \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) + x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\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 + ------|*atan(x)|
  |  /         2 \                           |          2|         |          2|        |
  |  |      4*x  | /  x             \        \     1 + x /         \     1 + x /        |
2*|3*|-1 + ------|*|------ + atan(x)| + ------------------ - ---------------------------|
  |  |          2| |     2          |              2                         2          |
  \  \     1 + x / \1 + x           /         1 + x                     1 + x           /
-----------------------------------------------------------------------------------------
                                                2                                        
                                        /     2\                                         
                                        \1 + x /
2(−12x2(2x2x2+1−1)atan⁡(x)x2+1+10x(x2x2+1−1)x2+1+3(xx2+1+atan⁡(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{atan}{\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{atan}{\left(x \right)}\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)\right)}{\left(x^{2} + 1\right)^{2}}
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Gráfico
Derivada de y=(xarctgx)/(1+x^(2))
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