Sr Examen

Derivada de (x*x*x)/arctgx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
 x*x*x 
-------
acot(x)
$$\frac{x x x}{\operatorname{acot}{\left(x \right)}}$$
((x*x)*x)/acot(x)
Gráfica
Primera derivada [src]
   2                  3       
2*x  + x*x           x        
---------- + -----------------
 acot(x)     /     2\     2   
             \1 + x /*acot (x)
$$\frac{x^{3}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} + \frac{2 x^{2} + x x}{\operatorname{acot}{\left(x \right)}}$$
Segunda derivada [src]
    /                         2 /       1   \\
    |                        x *|x - -------||
    |          3*x              \    acot(x)/|
2*x*|3 + ---------------- - -----------------|
    |    /     2\                   2        |
    |    \1 + x /*acot(x)   /     2\         |
    \                       \1 + x / *acot(x)/
----------------------------------------------
                   acot(x)                    
$$\frac{2 x \left(- \frac{x^{2} \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \frac{3 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + 3\right)}{\operatorname{acot}{\left(x \right)}}$$
Tercera derivada [src]
  /                          /                             2                    \                     \
  |                        3 |             3            4*x           6*x       |                     |
  |                       x *|-1 + ----------------- + ------ - ----------------|      2 /       1   \|
  |                          |     /     2\     2           2   /     2\        |   9*x *|x - -------||
  |          9*x             \     \1 + x /*acot (x)   1 + x    \1 + x /*acot(x)/        \    acot(x)/|
2*|3 + ---------------- + ------------------------------------------------------- - ------------------|
  |    /     2\                                      2                                      2         |
  |    \1 + x /*acot(x)                      /     2\                               /     2\          |
  \                                          \1 + x / *acot(x)                      \1 + x / *acot(x) /
-------------------------------------------------------------------------------------------------------
                                                acot(x)                                                
$$\frac{2 \left(\frac{x^{3} \left(\frac{4 x^{2}}{x^{2} + 1} - \frac{6 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - 1 + \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} - \frac{9 x^{2} \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \frac{9 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + 3\right)}{\operatorname{acot}{\left(x \right)}}$$
Gráfico
Derivada de (x*x*x)/arctgx