Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of 2x²
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Derivative of f(x)=1
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Derivative of e^x*x^2
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Derivative of 2*sqrt(x^3)
- Integral of d{x}:
- atan(1/(x-1))
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Identical expressions
- atan(one /(x- one))
- arc tangent of gent of (1 divide by (x minus 1))
- arc tangent of gent of (one divide by (x minus one))
- atan1/x-1
- atan(1 divide by (x-1))
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Similar expressions
- atan(1/(x+1))
- arctan(1/(x-1))
Derivative of atan(1/(x-1))
The solution
You have entered
[src]
/ 1 \
atan|-----|
\x - 1/
$$\operatorname{atan}{\left(\frac{1}{x - 1} \right)}$$
atan(1/(x - 1))
The first derivative
[src]
-1 ----------------------- / 1 \ 2 |1 + --------|*(x - 1) | 2| \ (x - 1) /
$$- \frac{1}{\left(1 + \frac{1}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)^{2}}$$
The second derivative
[src]
/ 1 \
2*|1 - -------------------------|
| / 1 \ 2|
| |1 + ---------|*(-1 + x) |
| | 2| |
\ \ (-1 + x) / /
---------------------------------
/ 1 \ 3
|1 + ---------|*(-1 + x)
| 2|
\ (-1 + x) /
$$\frac{2 \left(1 - \frac{1}{\left(1 + \frac{1}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)^{2}}\right)}{\left(1 + \frac{1}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)^{3}}$$
The third derivative
[src]
/ 4 7 \
2*|-3 - -------------------------- + -------------------------|
| 2 / 1 \ 2|
| / 1 \ 4 |1 + ---------|*(-1 + x) |
| |1 + ---------| *(-1 + x) | 2| |
| | 2| \ (-1 + x) / |
\ \ (-1 + x) / /
---------------------------------------------------------------
/ 1 \ 4
|1 + ---------|*(-1 + x)
| 2|
\ (-1 + x) /
$$\frac{2 \left(-3 + \frac{7}{\left(1 + \frac{1}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)^{2}} - \frac{4}{\left(1 + \frac{1}{\left(x - 1\right)^{2}}\right)^{2} \left(x - 1\right)^{4}}\right)}{\left(1 + \frac{1}{\left(x - 1\right)^{2}}\right) \left(x - 1\right)^{4}}$$
The graph