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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^6/6
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Derivative of x^3/x
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Derivative of (x-3)^4
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Identical expressions
- arcctg(((x- three))/((x^ two)+ four))
- arcctg(((x minus 3)) divide by ((x squared ) plus 4))
- arcctg(((x minus three)) divide by ((x to the power of two) plus four))
- arcctg(((x-3))/((x2)+4))
- arcctgx-3/x2+4
- arcctg(((x-3))/((x²)+4))
- arcctg(((x-3))/((x to the power of 2)+4))
- arcctgx-3/x^2+4
- arcctg(((x-3)) divide by ((x^2)+4))
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Similar expressions
- arcctg(((x-3))/((x^2)-4))
- arcctg(((x+3))/((x^2)+4))
Derivative of arcctg(((x-3))/((x^2)+4))
The solution
You have entered
[src]
/x - 3 \
acot|------|
| 2 |
\x + 4/
$$\operatorname{acot}{\left(\frac{x - 3}{x^{2} + 4} \right)}$$
d / /x - 3 \\ --|acot|------|| dx| | 2 || \ \x + 4//
$$\frac{d}{d x} \operatorname{acot}{\left(\frac{x - 3}{x^{2} + 4} \right)}$$
The first derivative
[src]
/ 1 2*x*(x - 3)\
-|------ - -----------|
| 2 2 |
|x + 4 / 2 \ |
\ \x + 4/ /
------------------------
2
(x - 3)
1 + ---------
2
/ 2 \
\x + 4/
$$- \frac{- \frac{2 x \left(x - 3\right)}{\left(x^{2} + 4\right)^{2}} + \frac{1}{x^{2} + 4}}{\frac{\left(x - 3\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1}$$
The second derivative
[src]
/ 2 \
| / 2*x*(-3 + x)\ |
| |-1 + ------------| *(-3 + x)|
| 2 | 2 | |
| 4*x *(-3 + x) \ 4 + x / |
2*|-3 + 3*x - ------------- + -----------------------------|
| 2 / 2\ |
| 4 + x | (-3 + x) | / 2\ |
| |1 + ---------|*\4 + x / |
| | 2| |
| | / 2\ | |
\ \ \4 + x / / /
------------------------------------------------------------
/ 2\ 2
| (-3 + x) | / 2\
|1 + ---------|*\4 + x /
| 2|
| / 2\ |
\ \4 + x / /
$$\frac{2 \left(- \frac{4 x^{2} \left(x - 3\right)}{x^{2} + 4} + 3 x + \frac{\left(x - 3\right) \left(\frac{2 x \left(x - 3\right)}{x^{2} + 4} - 1\right)^{2}}{\left(x^{2} + 4\right) \left(\frac{\left(x - 3\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)} - 3\right)}{\left(x^{2} + 4\right)^{2} \left(\frac{\left(x - 3\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)}$$
The third derivative
[src]
/ / 2 2 2\ \
| / 2*x*(-3 + x)\ | 2*(-3 + x) 8*x*(-3 + x) 12*x *(-3 + x) | 3 / 2 \|
| |-1 + ------------|*|1 - ----------- - ------------ + ---------------| / 2*x*(-3 + x)\ 2 / 2*x*(-3 + x)\ | 4*x *(-3 + x)||
| | 2 | | 2 2 2 | 4*|-1 + ------------| *(-3 + x) 4*|-1 + ------------|*(-3 + x)*|-3 + 3*x - -------------||
| 2 3 \ 4 + x / | 4 + x 4 + x / 2\ | | 2 | | 2 | | 2 ||
| 12*x 12*x*(-3 + x) 24*x *(-3 + x) \ \4 + x / / \ 4 + x / \ 4 + x / \ 4 + x /|
2*|3 - ------ - ------------- + -------------- - ---------------------------------------------------------------------- + -------------------------------- + ---------------------------------------------------------|
| 2 2 2 / 2\ 2 / 2\ 2 |
| 4 + x 4 + x / 2\ | (-3 + x) | / 2\ / 2\ 3 | (-3 + x) | / 2\ |
| \4 + x / |1 + ---------|*\4 + x / | (-3 + x) | / 2\ |1 + ---------|*\4 + x / |
| | 2| |1 + ---------| *\4 + x / | 2| |
| | / 2\ | | 2| | / 2\ | |
| \ \4 + x / / | / 2\ | \ \4 + x / / |
\ \ \4 + x / / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\ 2
| (-3 + x) | / 2\
|1 + ---------|*\4 + x /
| 2|
| / 2\ |
\ \4 + x / /
$$\frac{2 \cdot \left(\frac{24 x^{3} \left(x - 3\right)}{\left(x^{2} + 4\right)^{2}} - \frac{12 x^{2}}{x^{2} + 4} - \frac{12 x \left(x - 3\right)}{x^{2} + 4} + \frac{4 \left(x - 3\right)^{2} \left(\frac{2 x \left(x - 3\right)}{x^{2} + 4} - 1\right)^{3}}{\left(x^{2} + 4\right)^{3} \left(\frac{\left(x - 3\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)^{2}} + \frac{4 \left(x - 3\right) \left(\frac{2 x \left(x - 3\right)}{x^{2} + 4} - 1\right) \left(- \frac{4 x^{2} \left(x - 3\right)}{x^{2} + 4} + 3 x - 3\right)}{\left(x^{2} + 4\right)^{2} \left(\frac{\left(x - 3\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)} + 3 - \frac{\left(\frac{2 x \left(x - 3\right)}{x^{2} + 4} - 1\right) \left(\frac{12 x^{2} \left(x - 3\right)^{2}}{\left(x^{2} + 4\right)^{2}} - \frac{8 x \left(x - 3\right)}{x^{2} + 4} - \frac{2 \left(x - 3\right)^{2}}{x^{2} + 4} + 1\right)}{\left(x^{2} + 4\right) \left(\frac{\left(x - 3\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)}\right)}{\left(x^{2} + 4\right)^{2} \left(\frac{\left(x - 3\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)}$$
The graph