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How to use it?
- Derivative of:
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Derivative of sqrt(cos(x))
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Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of 5*tan(x)
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Derivative of (4x+1)/(3x-1)
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Identical expressions
- е^(arcctg(x- one)/(x+ one))
- е to the power of (arcctg(x minus 1) divide by (x plus 1))
- е to the power of (arcctg(x minus one) divide by (x plus one))
- е(arcctg(x-1)/(x+1))
- еarcctgx-1/x+1
- е^arcctgx-1/x+1
- е^(arcctg(x-1) divide by (x+1))
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Similar expressions
- е^(arcctg(x-1)/(x-1))
- е^(arcctg(x+1)/(x+1))
Derivative of е^(arcctg(x-1)/(x+1))
The solution
You have entered
[src]
acot(x - 1)
-----------
x + 1
E
$$e^{\frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}}$$
E^(acot(x - 1)/(x + 1))
The first derivative
[src]
acot(x - 1)
-----------
/ 1 acot(x - 1)\ x + 1
|- ---------------------- - -----------|*e
| / 2\ 2 |
\ \1 + (x - 1) /*(x + 1) (x + 1) /
$$\left(- \frac{1}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} - \frac{\operatorname{acot}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right) e^{\frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}}$$
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) / /
-------------------------------------------------------------------------------------------------------------
1 + x
$$\frac{\left(\frac{2 \left(x - 1\right)}{\left(\left(x - 1\right)^{2} + 1\right)^{2}} + \frac{\left(\frac{1}{\left(x - 1\right)^{2} + 1} + \frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}\right)^{2}}{x + 1} + \frac{2}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} + \frac{2 \operatorname{acot}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right) e^{\frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}}}{x + 1}$$
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) / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1 + x
$$- \frac{\left(\frac{8 \left(x - 1\right)^{2}}{\left(\left(x - 1\right)^{2} + 1\right)^{3}} + \frac{6 \left(x - 1\right)}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)^{2}} - \frac{2}{\left(\left(x - 1\right)^{2} + 1\right)^{2}} + \frac{6 \left(\frac{1}{\left(x - 1\right)^{2} + 1} + \frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}\right) \left(\frac{x - 1}{\left(\left(x - 1\right)^{2} + 1\right)^{2}} + \frac{1}{\left(x + 1\right) \left(\left(x - 1\right)^{2} + 1\right)} + \frac{\operatorname{acot}{\left(x - 1 \right)}}{\left(x + 1\right)^{2}}\right)}{x + 1} + \frac{\left(\frac{1}{\left(x - 1\right)^{2} + 1} + \frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}\right)^{3}}{\left(x + 1\right)^{2}} + \frac{6}{\left(x + 1\right)^{2} \left(\left(x - 1\right)^{2} + 1\right)} + \frac{6 \operatorname{acot}{\left(x - 1 \right)}}{\left(x + 1\right)^{3}}\right) e^{\frac{\operatorname{acot}{\left(x - 1 \right)}}{x + 1}}}{x + 1}$$
The graph