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е^(arcctg(x-1)/(x+1))
The derivative of the function/ е^(arcctg(x-1)/(x+1))

Derivative of е^(arcctg(x-1)/(x+1))

Function f() - derivative -N order at the point
v

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The solution

You have entered [src] 
 acot(x - 1)
 -----------
    x + 1   
E
eacot⁡(x−1)x+1e^{\frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}} 
E^(acot(x - 1)/(x + 1))
The graph
02468-8-6-4-2-10104000-2000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                                          acot(x - 1)
                                          -----------
/            1              acot(x - 1)\     x + 1   
|- ---------------------- - -----------|*e           
|  /           2\                    2 |             
\  \1 + (x - 1) /*(x + 1)     (x + 1)  /
(−1(x+1)((x−1)2+1)−acot⁡(x−1)(x+1)2)eacot⁡(x−1)x+1\left(- \frac{1}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} - \frac{\operatorname{acot}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right) e^{\frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}}
Simplify
The second derivative [src] 
/                              2                                                              \              
|/      1         acot(-1 + x)\                                                               |              
||------------- + ------------|                                                               |  acot(-1 + x)
||            2      1 + x    |                                                               |  ------------
|\1 + (-1 + x)                /               2              2*acot(-1 + x)      2*(-1 + x)   |     1 + x    
|------------------------------- + ----------------------- + -------------- + ----------------|*e            
|             1 + x                        /            2\             2                     2|              
|                                  (1 + x)*\1 + (-1 + x) /      (1 + x)       /            2\ |              
\                                                                             \1 + (-1 + x) / /              
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                                                    1 + x
(2(x−1)((x−1)2+1)2+(1(x−1)2+1+acot⁡(x−1)x+1)2x+1+2(x+1)((x−1)2+1)+2acot⁡(x−1)(x+1)2)eacot⁡(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{acot}{\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{acot}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right) e^{\frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}}}{x + 1}
Simplify
The third derivative [src] 
 /                                                   3                                                                                               /      1         acot(-1 + x)\ /           1              acot(-1 + x)        -1 + x     \\               
 |                     /      1         acot(-1 + x)\                                                                                              6*|------------- + ------------|*|----------------------- + ------------ + ----------------||               
 |                     |------------- + ------------|                                                                                                |            2      1 + x    | |        /            2\            2                    2||  acot(-1 + x) 
 |                     |            2      1 + x    |                                                            2                                   \1 + (-1 + x)                / |(1 + x)*\1 + (-1 + x) /     (1 + x)      /            2\ ||  ------------ 
 |         2           \1 + (-1 + x)                /    6*acot(-1 + x)              6                 8*(-1 + x)              6*(-1 + x)                                           \                                         \1 + (-1 + x) / /|     1 + x     
-|- ---------------- + ------------------------------- + -------------- + ------------------------ + ---------------- + ------------------------ + --------------------------------------------------------------------------------------------|*e             
 |                 2                      2                        3             2 /            2\                  3                          2                                              1 + x                                            |               
 |  /            2\                (1 + x)                  (1 + x)       (1 + x) *\1 + (-1 + x) /   /            2\            /            2\                                                                                                |               
 \  \1 + (-1 + x) /                                                                                  \1 + (-1 + x) /    (1 + x)*\1 + (-1 + x) /                                                                                                /               
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                                                                                                                             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+acot⁡(x−1)x+1)(x−1((x−1)2+1)2+1(x+1)((x−1)2+1)+acot⁡(x−1)(x+1)2)x+1+(1(x−1)2+1+acot⁡(x−1)x+1)3(x+1)2+6(x+1)2((x−1)2+1)+6acot⁡(x−1)(x+1)3)eacot⁡(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{acot}{\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{acot}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right)}{x + 1} + \frac{\left(\frac{1}{\left(x - 1\right)^{2} + 1} + \frac{\operatorname{acot}{\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{acot}{\left(x - 1 \right)}}{\left(x + 1\right)^{3}}\right) e^{\frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}}}{x + 1}
Simplify
The graph
Derivative of е^(arcctg(x-1)/(x+1))
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