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е^(arcctg(x-1/x+1))
Derivada de la función/ 1/x+1/ x-1/x/ е^(arcctg(x-1/x+1))

Derivada de е^(arcctg(x-1/x+1))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     /    1    \
 acot|x - - + 1|
     \    x    /
E
eacot⁡((x−1x)+1)e^{\operatorname{acot}{\left(\left(x - \frac{1}{x}\right) + 1 \right)}} 
E^acot(x - 1/x + 1)
Gráfica
02468-8-6-4-2-1010-2020
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Primera derivada [src] 
               /    1    \ 
           acot|x - - + 1| 
 /    1 \      \    x    / 
-|1 + --|*e                
 |     2|                  
 \    x /                  
---------------------------
                     2     
          /    1    \      
      1 + |x - - + 1|      
          \    x    /
−(1+1x2)eacot⁡((x−1x)+1)((x−1x)+1)2+1- \frac{\left(1 + \frac{1}{x^{2}}\right) e^{\operatorname{acot}{\left(\left(x - \frac{1}{x}\right) + 1 \right)}}}{\left(\left(x - \frac{1}{x}\right) + 1\right)^{2} + 1}
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Segunda derivada [src] 
/                2                 2            \                 
|        /    1 \          /    1 \  /        1\|                 
|        |1 + --|        2*|1 + --| *|1 + x - -||      /        1\
|        |     2|          |     2|  \        x/|  acot|1 + x - -|
|2       \    x /          \    x /             |      \        x/
|-- + ---------------- + -----------------------|*e               
| 3                  2                      2   |                 
|x        /        1\            /        1\    |                 
|     1 + |1 + x - -|        1 + |1 + x - -|    |                 
\         \        x/            \        x/    /                 
------------------------------------------------------------------
                                        2                         
                             /        1\                          
                         1 + |1 + x - -|                          
                             \        x/
(2(1+1x2)2(x+1−1x)(x+1−1x)2+1+(1+1x2)2(x+1−1x)2+1+2x3)eacot⁡(x+1−1x)(x+1−1x)2+1\frac{\left(\frac{2 \left(1 + \frac{1}{x^{2}}\right)^{2} \left(x + 1 - \frac{1}{x}\right)}{\left(x + 1 - \frac{1}{x}\right)^{2} + 1} + \frac{\left(1 + \frac{1}{x^{2}}\right)^{2}}{\left(x + 1 - \frac{1}{x}\right)^{2} + 1} + \frac{2}{x^{3}}\right) e^{\operatorname{acot}{\left(x + 1 - \frac{1}{x} \right)}}}{\left(x + 1 - \frac{1}{x}\right)^{2} + 1}
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Tercera derivada [src] 
/                    3                    3                3            2                                     3                                      \                 
|            /    1 \             /    1 \         /    1 \  /        1\            /    1 \          /    1 \  /        1\      /    1 \ /        1\|                 
|            |1 + --|           2*|1 + --|       8*|1 + --| *|1 + x - -|          6*|1 + --|        6*|1 + --| *|1 + x - -|   12*|1 + --|*|1 + x - -||      /        1\
|            |     2|             |     2|         |     2|  \        x/            |     2|          |     2|  \        x/      |     2| \        x/|  acot|1 + x - -|
|  6         \    x /             \    x /         \    x /                         \    x /          \    x /                   \    x /            |      \        x/
|- -- - ------------------- + ---------------- - ------------------------ - --------------------- - ----------------------- - -----------------------|*e               
|   4                     2                  2                       2         /               2\                       2         /               2\ |                 
|  x    /               2\        /        1\      /               2\        3 |    /        1\ |     /               2\        3 |    /        1\ | |                 
|       |    /        1\ |    1 + |1 + x - -|      |    /        1\ |       x *|1 + |1 + x - -| |     |    /        1\ |       x *|1 + |1 + x - -| | |                 
|       |1 + |1 + x - -| |        \        x/      |1 + |1 + x - -| |          \    \        x/ /     |1 + |1 + x - -| |          \    \        x/ / |                 
\       \    \        x/ /                         \    \        x/ /                                 \    \        x/ /                             /                 
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                           2                                                                           
                                                                                /        1\                                                                            
                                                                            1 + |1 + x - -|                                                                            
                                                                                \        x/
(2(1+1x2)3(x+1−1x)2+1−8(1+1x2)3(x+1−1x)2((x+1−1x)2+1)2−6(1+1x2)3(x+1−1x)((x+1−1x)2+1)2−(1+1x2)3((x+1−1x)2+1)2−12(1+1x2)(x+1−1x)x3((x+1−1x)2+1)−6(1+1x2)x3((x+1−1x)2+1)−6x4)eacot⁡(x+1−1x)(x+1−1x)2+1\frac{\left(\frac{2 \left(1 + \frac{1}{x^{2}}\right)^{3}}{\left(x + 1 - \frac{1}{x}\right)^{2} + 1} - \frac{8 \left(1 + \frac{1}{x^{2}}\right)^{3} \left(x + 1 - \frac{1}{x}\right)^{2}}{\left(\left(x + 1 - \frac{1}{x}\right)^{2} + 1\right)^{2}} - \frac{6 \left(1 + \frac{1}{x^{2}}\right)^{3} \left(x + 1 - \frac{1}{x}\right)}{\left(\left(x + 1 - \frac{1}{x}\right)^{2} + 1\right)^{2}} - \frac{\left(1 + \frac{1}{x^{2}}\right)^{3}}{\left(\left(x + 1 - \frac{1}{x}\right)^{2} + 1\right)^{2}} - \frac{12 \left(1 + \frac{1}{x^{2}}\right) \left(x + 1 - \frac{1}{x}\right)}{x^{3} \left(\left(x + 1 - \frac{1}{x}\right)^{2} + 1\right)} - \frac{6 \left(1 + \frac{1}{x^{2}}\right)}{x^{3} \left(\left(x + 1 - \frac{1}{x}\right)^{2} + 1\right)} - \frac{6}{x^{4}}\right) e^{\operatorname{acot}{\left(x + 1 - \frac{1}{x} \right)}}}{\left(x + 1 - \frac{1}{x}\right)^{2} + 1}
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Gráfico
Derivada de е^(arcctg(x-1/x+1))
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