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y=(arctgx+x)^2

Derivada de y=(arctgx+x)^2

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Solución

Ha introducido [src]
             2
(acot(x) + x) 
$$\left(x + \operatorname{acot}{\left(x \right)}\right)^{2}$$
(acot(x) + x)^2
Gráfica
Primera derivada [src]
/      2   \              
|2 - ------|*(acot(x) + x)
|         2|              
\    1 + x /              
$$\left(2 - \frac{2}{x^{2} + 1}\right) \left(x + \operatorname{acot}{\left(x \right)}\right)$$
Segunda derivada [src]
  /            2                    \
  |/      1   \    2*x*(x + acot(x))|
2*||1 - ------|  + -----------------|
  ||         2|                2    |
  |\    1 + x /        /     2\     |
  \                    \1 + x /     /
$$2 \left(\frac{2 x \left(x + \operatorname{acot}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} + \left(1 - \frac{1}{x^{2} + 1}\right)^{2}\right)$$
Tercera derivada [src]
  /                          2                        \
  |        /      1   \   4*x *(x + acot(x))          |
4*|x + 3*x*|1 - ------| - ------------------ + acot(x)|
  |        |         2|              2                |
  \        \    1 + x /         1 + x                 /
-------------------------------------------------------
                               2                       
                       /     2\                        
                       \1 + x /                        
$$\frac{4 \left(- \frac{4 x^{2} \left(x + \operatorname{acot}{\left(x \right)}\right)}{x^{2} + 1} + 3 x \left(1 - \frac{1}{x^{2} + 1}\right) + x + \operatorname{acot}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}$$
Gráfico
Derivada de y=(arctgx+x)^2