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e^(arctg((x-1)/(x+1)))
Derivada de la función/ arctg/ (x-1)/ (x+1)/ e^(arctg((x-1)/(x+1)))

Derivada de e^(arctg((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/
E
eatan⁡(x−1x+1)e^{\operatorname{atan}{\left(\frac{x - 1}{x + 1} \right)}} 
E^atan((x - 1)/(x + 1))
Gráfica
02468-8-6-4-2-101005
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                        /x - 1\
                    atan|-----|
/  1      x - 1  \      \x + 1/
|----- - --------|*e           
|x + 1          2|             
\        (x + 1) /             
-------------------------------
                     2         
              (x - 1)          
          1 + --------         
                     2         
              (x + 1)
(−x−1(x+1)2+1x+1)eatan⁡(x−1x+1)(x−1)2(x+1)2+1\frac{\left(- \frac{x - 1}{\left(x + 1\right)^{2}} + \frac{1}{x + 1}\right) e^{\operatorname{atan}{\left(\frac{x - 1}{x + 1} \right)}}}{\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1}
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Segunda derivada [src] 
              /          -1 + x               /     -1 + x\\      /-1 + x\
              |     -1 + ------    2*(-1 + x)*|-1 + ------||  atan|------|
/     -1 + x\ |          1 + x                \     1 + x /|      \1 + x /
|-1 + ------|*|2 + ------------- - ------------------------|*e            
\     1 + x / |                2           /            2\ |              
              |        (-1 + x)            |    (-1 + x) | |              
              |    1 + ---------   (1 + x)*|1 + ---------| |              
              |                2           |            2| |              
              \         (1 + x)            \     (1 + x) / /              
--------------------------------------------------------------------------
                                  /            2\                         
                                2 |    (-1 + x) |                         
                         (1 + x) *|1 + ---------|                         
                                  |            2|                         
                                  \     (1 + x) /
(x−1x+1−1)(−2(x−1)(x−1x+1−1)(x+1)((x−1)2(x+1)2+1)+x−1x+1−1(x−1)2(x+1)2+1+2)eatan⁡(x−1x+1)(x+1)2((x−1)2(x+1)2+1)\frac{\left(\frac{x - 1}{x + 1} - 1\right) \left(- \frac{2 \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)} + \frac{\frac{x - 1}{x + 1} - 1}{\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1} + 2\right) e^{\operatorname{atan}{\left(\frac{x - 1}{x + 1} \right)}}}{\left(x + 1\right)^{2} \left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)}
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Tercera derivada [src] 
              /                                            /                           2\                                                                                    \              
              |                   2                        |    4*(-1 + x)   3*(-1 + x) |                            2                  2                                    |              
              |      /     -1 + x\       /     -1 + x\   2*|1 - ---------- + -----------|             2 /     -1 + x\      /     -1 + x\                        /     -1 + x\|      /-1 + x\
              |      |-1 + ------|     6*|-1 + ------|     |      1 + x               2 |   8*(-1 + x) *|-1 + ------|    6*|-1 + ------| *(-1 + x)   8*(-1 + x)*|-1 + ------||  atan|------|
/     -1 + x\ |      \     1 + x /       \     1 + x /     \                   (1 + x)  /               \     1 + x /      \     1 + x /                        \     1 + x /|      \1 + x /
|-1 + ------|*|-6 - ---------------- - --------------- + -------------------------------- - -------------------------- + ------------------------- + ------------------------|*e            
\     1 + x / |                    2                2                         2                                     2                            2           /            2\ |              
              |     /            2\         (-1 + x)                  (-1 + x)                       /            2\              /            2\            |    (-1 + x) | |              
              |     |    (-1 + x) |     1 + ---------             1 + ---------                    2 |    (-1 + x) |              |    (-1 + x) |    (1 + x)*|1 + ---------| |              
              |     |1 + ---------|                 2                         2             (1 + x) *|1 + ---------|      (1 + x)*|1 + ---------|            |            2| |              
              |     |            2|          (1 + x)                   (1 + x)                       |            2|              |            2|            \     (1 + x) / |              
              \     \     (1 + x) /                                                                  \     (1 + x) /              \     (1 + x) /                            /              
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                           /            2\                                                                                  
                                                                                         3 |    (-1 + x) |                                                                                  
                                                                                  (1 + x) *|1 + ---------|                                                                                  
                                                                                           |            2|                                                                                  
                                                                                           \     (1 + x) /
(x−1x+1−1)(−8(x−1)2(x−1x+1−1)2(x+1)2((x−1)2(x+1)2+1)2+6(x−1)(x−1x+1−1)2(x+1)((x−1)2(x+1)2+1)2+8(x−1)(x−1x+1−1)(x+1)((x−1)2(x+1)2+1)−(x−1x+1−1)2((x−1)2(x+1)2+1)2−6(x−1x+1−1)(x−1)2(x+1)2+1−6+2(3(x−1)2(x+1)2−4(x−1)x+1+1)(x−1)2(x+1)2+1)eatan⁡(x−1x+1)(x+1)3((x−1)2(x+1)2+1)\frac{\left(\frac{x - 1}{x + 1} - 1\right) \left(- \frac{8 \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{6 \left(x - 1\right) \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{\left(x + 1\right) \left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)^{2}} + \frac{8 \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)} - \frac{\left(\frac{x - 1}{x + 1} - 1\right)^{2}}{\left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)^{2}} - \frac{6 \left(\frac{x - 1}{x + 1} - 1\right)}{\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1} - 6 + \frac{2 \left(\frac{3 \left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} - \frac{4 \left(x - 1\right)}{x + 1} + 1\right)}{\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1}\right) e^{\operatorname{atan}{\left(\frac{x - 1}{x + 1} \right)}}}{\left(x + 1\right)^{3} \left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)}
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Gráfico
Derivada de e^(arctg((x-1)/(x+1)))
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