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

Derivada de y=(arctg^2)1/x

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

Gráfico:

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Solución

Ha introducido [src] 
    2   
atan (x)
--------
   x
atan⁡2(x)x\frac{\operatorname{atan}^{2}{\left(x \right)}}{x} 
atan(x)^2/x
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      2                
  atan (x)   2*atan(x) 
- -------- + ----------
      2        /     2\
     x       x*\1 + x /
2atan⁡(x)x(x2+1)−atan⁡2(x)x2\frac{2 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}
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Segunda derivada [src] 
  /    2                                   \
  |atan (x)   -1 + 2*x*atan(x)   2*atan(x) |
2*|-------- - ---------------- - ----------|
  |    2                 2         /     2\|
  |   x          /     2\        x*\1 + x /|
  \              \1 + x /                  /
--------------------------------------------
                     x
2(−2xatan⁡(x)−1(x2+1)2−2atan⁡(x)x(x2+1)+atan⁡2(x)x2)x\frac{2 \left(- \frac{2 x \operatorname{atan}{\left(x \right)} - 1}{\left(x^{2} + 1\right)^{2}} - \frac{2 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right)}{x}
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Tercera derivada [src] 
  /                 /            2                  \                                     \
  |                 | 3*x     4*x *atan(x)          |                                     |
  |               2*|------ - ------------ + atan(x)|                                     |
  |        2        |     2           2             |                                     |
  |  3*atan (x)     \1 + x       1 + x              /   3*(-1 + 2*x*atan(x))    6*atan(x) |
2*|- ---------- - ----------------------------------- + -------------------- + -----------|
  |       3                            2                              2         2 /     2\|
  |      x                     /     2\                       /     2\         x *\1 + x /|
  \                            \1 + x /                     x*\1 + x /                    /
-------------------------------------------------------------------------------------------
                                             x
2(−2(−4x2atan⁡(x)x2+1+3xx2+1+atan⁡(x))(x2+1)2+3(2xatan⁡(x)−1)x(x2+1)2+6atan⁡(x)x2(x2+1)−3atan⁡2(x)x3)x\frac{2 \left(- \frac{2 \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{x \left(x^{2} + 1\right)^{2}} + \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} - \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{x^{3}}\right)}{x}
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Gráfico
Derivada de y=(arctg^2)1/x
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