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(x*x+1)/arctgx
Derivada de la función/ x*x+1/ arctg/ (x*x+1)/arctgx

Derivada de (x*x+1)/arctgx

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

Gráfico:

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Solución

Ha introducido [src] 
x*x + 1
-------
acot(x)
xx+1acot⁡(x)\frac{x x + 1}{\operatorname{acot}{\left(x \right)}} 
(x*x + 1)/acot(x)
Gráfica
02468-8-6-4-2-1010-20002000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  2*x          x*x + 1     
------- + -----------------
acot(x)   /     2\     2   
          \1 + x /*acot (x)
2xacot⁡(x)+xx+1(x2+1)acot⁡2(x)\frac{2 x}{\operatorname{acot}{\left(x \right)}} + \frac{x x + 1}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}
Simplificar
Segunda derivada [src] 
  /             1                         \
  |      x - -------                      |
  |          acot(x)            2*x       |
2*|1 - ---------------- + ----------------|
  |    /     2\           /     2\        |
  \    \1 + x /*acot(x)   \1 + x /*acot(x)/
-------------------------------------------
                  acot(x)
2(2x(x2+1)acot⁡(x)−x−1acot⁡(x)(x2+1)acot⁡(x)+1)acot⁡(x)\frac{2 \left(\frac{2 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{x - \frac{1}{\operatorname{acot}{\left(x \right)}}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + 1\right)}{\operatorname{acot}{\left(x \right)}}
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Tercera derivada [src] 
  /                                                        /       1   \\
  |                            2                       6*x*|x - -------||
  |            3            4*x           6*x              \    acot(x)/|
2*|2 + ----------------- + ------ - ---------------- - -----------------|
  |    /     2\     2           2   /     2\                      2     |
  \    \1 + x /*acot (x)   1 + x    \1 + x /*acot(x)         1 + x      /
-------------------------------------------------------------------------
                            /     2\     2                               
                            \1 + x /*acot (x)
2(4x2x2+1−6x(x−1acot⁡(x))x2+1−6x(x2+1)acot⁡(x)+2+3(x2+1)acot⁡2(x))(x2+1)acot⁡2(x)\frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - \frac{6 x \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right)}{x^{2} + 1} - \frac{6 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + 2 + \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right)}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}
Simplificar
Gráfico
Derivada de (x*x+1)/arctgx
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