Sr Examen

Otras calculadoras


arctan((x+1)/(x-1))

Derivada de arctan((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)   
$$\frac{\frac{1}{x - 1} - \frac{x + 1}{\left(x - 1\right)^{2}}}{1 + \frac{\left(x + 1\right)^{2}}{\left(x - 1\right)^{2}}}$$
Segunda derivada [src]
                /              /    1 + x \  \
                |      (1 + x)*|1 - ------|  |
   /    1 + x \ |              \    -1 + x/  |
-2*|1 - ------|*|1 + ------------------------|
   \    -1 + x/ |    /            2\         |
                |    |     (1 + x) |         |
                |    |1 + ---------|*(-1 + x)|
                |    |            2|         |
                \    \    (-1 + x) /         /
----------------------------------------------
          /            2\                     
          |     (1 + x) |         2           
          |1 + ---------|*(-1 + x)            
          |            2|                     
          \    (-1 + x) /                     
$$- \frac{2 \left(1 - \frac{x + 1}{x - 1}\right) \left(1 + \frac{\left(1 - \frac{x + 1}{x - 1}\right) \left(x + 1\right)}{\left(1 + \frac{\left(x + 1\right)^{2}}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)}\right)}{\left(1 + \frac{\left(x + 1\right)^{2}}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)^{2}}$$
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 + ---------          |     (1 + x) |          2   |1 + ---------|*(-1 + x)|
               |                      2          |1 + ---------| *(-1 + x)    |            2|         |
               |              (-1 + x)           |            2|              \    (-1 + x) /         |
               \                                 \    (-1 + x) /                                      /
-------------------------------------------------------------------------------------------------------
                                       /            2\                                                 
                                       |     (1 + x) |         3                                       
                                       |1 + ---------|*(-1 + x)                                        
                                       |            2|                                                 
                                       \    (-1 + x) /                                                 
$$\frac{2 \left(1 - \frac{x + 1}{x - 1}\right) \left(3 + \frac{4 \left(1 - \frac{x + 1}{x - 1}\right) \left(x + 1\right)}{\left(1 + \frac{\left(x + 1\right)^{2}}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)} - \frac{1 - \frac{4 \left(x + 1\right)}{x - 1} + \frac{3 \left(x + 1\right)^{2}}{\left(x - 1\right)^{2}}}{1 + \frac{\left(x + 1\right)^{2}}{\left(x - 1\right)^{2}}} + \frac{4 \left(1 - \frac{x + 1}{x - 1}\right)^{2} \left(x + 1\right)^{2}}{\left(1 + \frac{\left(x + 1\right)^{2}}{\left(x - 1\right)^{2}}\right)^{2} \left(x - 1\right)^{2}}\right)}{\left(1 + \frac{\left(x + 1\right)^{2}}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)^{3}}$$
Gráfico
Derivada de arctan((x+1)/(x-1))