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(x(xarctgx-1)+arctgx)/2
Derivada de la función/ arctg/ ctgx-1/ (x(xarctgx-1)+arctgx)/2

Derivada de (x(xarctgx-1)+arctgx)/2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
x*(x*atan(x) - 1) + acot(x)
---------------------------
             2
x(xatan⁡(x)−1)+acot⁡(x)2\frac{x \left(x \operatorname{atan}{\left(x \right)} - 1\right) + \operatorname{acot}{\left(x \right)}}{2} 
(x*(x*atan(x) - 1) + acot(x))/2
Gráfica
02468-8-6-4-2-1010-200200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                     /  x             \            
                   x*|------ + atan(x)|            
                     |     2          |            
  1       1          \1 + x           /   x*atan(x)
- - - ---------- + -------------------- + ---------
  2     /     2\            2                 2    
      2*\1 + x /
x(xx2+1+atan⁡(x))2+xatan⁡(x)2−12−12(x2+1)\frac{x \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right)}{2} + \frac{x \operatorname{atan}{\left(x \right)}}{2} - \frac{1}{2} - \frac{1}{2 \left(x^{2} + 1\right)}
Simplificar
Segunda derivada [src] 
                       /        2  \          
                       |       x   |          
                     x*|-1 + ------|          
                       |          2|          
  x          x         \     1 + x /          
------ + --------- - --------------- + atan(x)
     2           2             2              
1 + x    /     2\         1 + x               
         \1 + x /
−x(x2x2+1−1)x2+1+xx2+1+x(x2+1)2+atan⁡(x)- \frac{x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + \frac{x}{x^{2} + 1} + \frac{x}{\left(x^{2} + 1\right)^{2}} + \operatorname{atan}{\left(x \right)}
Simplificar
Tercera derivada [src] 
                                       /        2  \
                                     2 |       x   |
                                  4*x *|-1 + ------|
                   2         2         |          2|
      1         4*x       3*x          \     1 + x /
3 + ------ - --------- - ------ + ------------------
         2           2        2              2      
    1 + x    /     2\    1 + x          1 + x       
             \1 + x /                               
----------------------------------------------------
                            2                       
                       1 + x
4x2(x2x2+1−1)x2+1−3x2x2+1−4x2(x2+1)2+3+1x2+1x2+1\frac{\frac{4 x^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{3 x^{2}}{x^{2} + 1} - \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 3 + \frac{1}{x^{2} + 1}}{x^{2} + 1}
Simplificar
Gráfico
Derivada de (x(xarctgx-1)+arctgx)/2
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