Sr Examen

Otras calculadoras

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

Derivada de е^(arctg(x-1)/(x+1))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 atan(x - 1)
 -----------
    x + 1   
E
eatan⁡(x−1)x+1e^{\frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}} 
E^(atan(x - 1)/(x + 1))
Gráfica
02468-8-6-4-2-1010-25000002500000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                        atan(x - 1)
                                        -----------
/          1              atan(x - 1)\     x + 1   
|---------------------- - -----------|*e           
|/           2\                    2 |             
\\1 + (x - 1) /*(x + 1)     (x + 1)  /
(1(x+1)((x−1)2+1)−atan⁡(x−1)(x+1)2)eatan⁡(x−1)x+1\left(\frac{1}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right) e^{\frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}}
Simplificar
Segunda derivada [src] 
/                              2                                                              \              
|/      1         atan(-1 + x)\                                                               |              
||------------- - ------------|                                                               |  atan(-1 + x)
||            2      1 + x    |                                                               |  ------------
|\1 + (-1 + x)                /               2                 2*(-1 + x)      2*atan(-1 + x)|     1 + x    
|------------------------------- - ----------------------- - ---------------- + --------------|*e            
|             1 + x                        /            2\                  2             2   |              
|                                  (1 + x)*\1 + (-1 + x) /   /            2\       (1 + x)    |              
\                                                            \1 + (-1 + x) /                  /              
-------------------------------------------------------------------------------------------------------------
                                                    1 + x
(−2(x−1)((x−1)2+1)2+(1(x−1)2+1−atan⁡(x−1)x+1)2x+1−2(x+1)((x−1)2+1)+2atan⁡(x−1)(x+1)2)eatan⁡(x−1)x+1x+1\frac{\left(- \frac{2 \left(x - 1\right)}{\left(\left(x - 1\right)^{2} + 1\right)^{2}} + \frac{\left(\frac{1}{\left(x - 1\right)^{2} + 1} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}\right)^{2}}{x + 1} - \frac{2}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} + \frac{2 \operatorname{atan}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right) e^{\frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}}}{x + 1}
Simplificar
Tercera derivada [src] 
/                                                   3                                                                    /      1         atan(-1 + x)\ /           1                   -1 + x        atan(-1 + x)\                           \              
|                     /      1         atan(-1 + x)\                                                                   6*|------------- - ------------|*|----------------------- + ---------------- - ------------|                           |              
|                     |------------- - ------------|                                                                     |            2      1 + x    | |        /            2\                  2            2  |                           |  atan(-1 + x)
|                     |            2      1 + x    |                                                            2        \1 + (-1 + x)                / |(1 + x)*\1 + (-1 + x) /   /            2\      (1 + x)   |                           |  ------------
|         2           \1 + (-1 + x)                /    6*atan(-1 + x)              6                 8*(-1 + x)                                        \                          \1 + (-1 + x) /                /          6*(-1 + x)       |     1 + x    
|- ---------------- + ------------------------------- - -------------- + ------------------------ + ---------------- - -------------------------------------------------------------------------------------------- + ------------------------|*e            
|                 2                      2                        3             2 /            2\                  3                                              1 + x                                                                      2|              
|  /            2\                (1 + x)                  (1 + x)       (1 + x) *\1 + (-1 + x) /   /            2\                                                                                                           /            2\ |              
\  \1 + (-1 + x) /                                                                                  \1 + (-1 + x) /                                                                                                   (1 + x)*\1 + (-1 + x) / /              
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                            1 + x
(8(x−1)2((x−1)2+1)3+6(x−1)(x+1)((x−1)2+1)2−2((x−1)2+1)2−6(1(x−1)2+1−atan⁡(x−1)x+1)(x−1((x−1)2+1)2+1(x+1)((x−1)2+1)−atan⁡(x−1)(x+1)2)x+1+(1(x−1)2+1−atan⁡(x−1)x+1)3(x+1)2+6(x+1)2((x−1)2+1)−6atan⁡(x−1)(x+1)3)eatan⁡(x−1)x+1x+1\frac{\left(\frac{8 \left(x - 1\right)^{2}}{\left(\left(x - 1\right)^{2} + 1\right)^{3}} + \frac{6 \left(x - 1\right)}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)^{2}} - \frac{2}{\left(\left(x - 1\right)^{2} + 1\right)^{2}} - \frac{6 \left(\frac{1}{\left(x - 1\right)^{2} + 1} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}\right) \left(\frac{x - 1}{\left(\left(x - 1\right)^{2} + 1\right)^{2}} + \frac{1}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right)}{x + 1} + \frac{\left(\frac{1}{\left(x - 1\right)^{2} + 1} - \frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}\right)^{3}}{\left(x + 1\right)^{2}} + \frac{6}{\left(x + 1\right)^{2} \left(\left(x - 1\right)^{2} + 1\right)} - \frac{6 \operatorname{atan}{\left(x - 1 \right)}}{\left(x + 1\right)^{3}}\right) e^{\frac{\operatorname{atan}{\left(x - 1 \right)}}{x + 1}}}{x + 1}
Simplificar
Gráfico
Derivada de е^(arctg(x-1)/(x+1))
    © Sr Examen – Калькулятор