Sr Examen

Otras calculadoras


atan((x-1)/(x+1))

Derivada de atan((x-1)/(x+1))

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

Gráfico:

interior superior

Definida a trozos:

Solución

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