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How to use it?
- Derivative of:
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Derivative of 4/x^3
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Derivative of (x+3)^2*(x+5)-1
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Derivative of x^3+2
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Derivative of x^(-2)
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Identical expressions
- e^(arctg((x- one)/(x+ one)))
- e to the power of (arctg((x minus 1) divide by (x plus 1)))
- e to the power of (arctg((x minus one) divide by (x plus one)))
- e(arctg((x-1)/(x+1)))
- earctgx-1/x+1
- e^arctgx-1/x+1
- e^(arctg((x-1) divide by (x+1)))
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Similar expressions
- e^(arctg((x+1)/(x+1)))
- e^(arctg((x-1)/(x-1)))
Derivative of e^(arctg((x-1)/(x+1)))
The solution
You have entered
[src]
/x - 1\
atan|-----|
\x + 1/
E
$$e^{\operatorname{atan}{\left(\frac{x - 1}{x + 1} \right)}}$$
E^atan((x - 1)/(x + 1))
The first derivative
[src]
/x - 1\
atan|-----|
/ 1 x - 1 \ \x + 1/
|----- - --------|*e
|x + 1 2|
\ (x + 1) /
-------------------------------
2
(x - 1)
1 + --------
2
(x + 1)
$$\frac{\left(- \frac{x - 1}{\left(x + 1\right)^{2}} + \frac{1}{x + 1}\right) e^{\operatorname{atan}{\left(\frac{x - 1}{x + 1} \right)}}}{\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1}$$
The second derivative
[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) /
$$\frac{\left(\frac{x - 1}{x + 1} - 1\right) \left(- \frac{2 \left(x - 1\right) \left(\frac{x - 1}{x + 1} - 1\right)}{\left(x + 1\right) \left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)} + \frac{\frac{x - 1}{x + 1} - 1}{\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1} + 2\right) e^{\operatorname{atan}{\left(\frac{x - 1}{x + 1} \right)}}}{\left(x + 1\right)^{2} \left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)}$$
The third derivative
[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) /
$$\frac{\left(\frac{x - 1}{x + 1} - 1\right) \left(- \frac{8 \left(x - 1\right)^{2} \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{\left(x + 1\right)^{2} \left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)^{2}} + \frac{6 \left(x - 1\right) \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{\left(x + 1\right) \left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)^{2}} + \frac{8 \left(x - 1\right) \left(\frac{x - 1}{x + 1} - 1\right)}{\left(x + 1\right) \left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)} - \frac{\left(\frac{x - 1}{x + 1} - 1\right)^{2}}{\left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)^{2}} - \frac{6 \left(\frac{x - 1}{x + 1} - 1\right)}{\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1} - 6 + \frac{2 \left(\frac{3 \left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} - \frac{4 \left(x - 1\right)}{x + 1} + 1\right)}{\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1}\right) e^{\operatorname{atan}{\left(\frac{x - 1}{x + 1} \right)}}}{\left(x + 1\right)^{3} \left(\frac{\left(x - 1\right)^{2}}{\left(x + 1\right)^{2}} + 1\right)}$$
The graph