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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of 5-7x
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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 x*e^x+11
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Identical expressions
- (x- two)arctg(one /(x- two))
- (x minus 2)arctg(1 divide by (x minus 2))
- (x minus two)arctg(one divide by (x minus two))
- x-2arctg1/x-2
- (x-2)arctg(1 divide by (x-2))
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Similar expressions
- (x-2)arctg(1/(x+2))
- (x+2)arctg(1/(x-2))
Derivative of (x-2)arctg(1/(x-2))
The solution
You have entered
[src]
/ 1 \
(x - 2)*atan|-----|
\x - 2/
$$\left(x - 2\right) \operatorname{atan}{\left(\frac{1}{x - 2} \right)}$$
(x - 2)*atan(1/(x - 2))
The first derivative
[src]
1 / 1 \ - ---------------------- + atan|-----| / 1 \ \x - 2/ |1 + --------|*(x - 2) | 2| \ (x - 2) /
$$\operatorname{atan}{\left(\frac{1}{x - 2} \right)} - \frac{1}{\left(1 + \frac{1}{\left(x - 2\right)^{2}}\right) \left(x - 2\right)}$$
The second derivative
[src]
-2
--------------------------
2
/ 1 \ 4
|1 + ---------| *(-2 + x)
| 2|
\ (-2 + x) /
$$- \frac{2}{\left(1 + \frac{1}{\left(x - 2\right)^{2}}\right)^{2} \left(x - 2\right)^{4}}$$
The third derivative
[src]
/ 4 4 \
2*|- -------------------------- + -------------------------|
| 2 / 1 \ 2|
| / 1 \ 4 |1 + ---------|*(-2 + x) |
| |1 + ---------| *(-2 + x) | 2| |
| | 2| \ (-2 + x) / |
\ \ (-2 + x) / /
------------------------------------------------------------
/ 1 \ 3
|1 + ---------|*(-2 + x)
| 2|
\ (-2 + x) /
$$\frac{2 \left(\frac{4}{\left(1 + \frac{1}{\left(x - 2\right)^{2}}\right) \left(x - 2\right)^{2}} - \frac{4}{\left(1 + \frac{1}{\left(x - 2\right)^{2}}\right)^{2} \left(x - 2\right)^{4}}\right)}{\left(1 + \frac{1}{\left(x - 2\right)^{2}}\right) \left(x - 2\right)^{3}}$$
The graph