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How to use it?
- Derivative of:
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Derivative of 5*x^2-2/sqrt(x)+sin(pi/4)
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Derivative of e^(-2*x)
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Derivative of e^t
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Derivative of e^(-x)*cos(x)
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Identical expressions
- (arctan(x))/(x^ two +x)
- (arc tangent of (x)) divide by (x squared plus x)
- (arc tangent of (x)) divide by (x to the power of two plus x)
- (arctan(x))/(x2+x)
- arctanx/x2+x
- (arctan(x))/(x²+x)
- (arctan(x))/(x to the power of 2+x)
- arctanx/x^2+x
- (arctan(x)) divide by (x^2+x)
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Similar expressions
- (arctan(x))/(x^2-x)
Derivative of (arctan(x))/(x^2+x)
The solution
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[src]
atan(x) ------- 2 x + x
$$\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + x}$$
d /atan(x)\ --|-------| dx| 2 | \ x + x/
$$\frac{d}{d x} \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + x}$$
The first derivative
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1 (-1 - 2*x)*atan(x)
----------------- + ------------------
/ 2\ / 2 \ 2
\1 + x /*\x + x/ / 2 \
\x + x/
$$\frac{\left(- 2 x - 1\right) \operatorname{atan}{\left(x \right)}}{\left(x^{2} + x\right)^{2}} + \frac{1}{\left(x^{2} + 1\right) \left(x^{2} + x\right)}$$
The second derivative
[src]
/ / 2\ \
| | (1 + 2*x) | |
| |1 - ----------|*atan(x)|
| 1 1 + 2*x \ x*(1 + x) / |
-2*|--------- + ------------------- + ------------------------|
| 2 2 / 2\ 2 |
|/ 2\ x *(1 + x)*\1 + x / x *(1 + x) |
\\1 + x / /
---------------------------------------------------------------
1 + x
$$- \frac{2 \left(\frac{\left(1 - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}\right) \operatorname{atan}{\left(x \right)}}{x^{2} \left(x + 1\right)} + \frac{1}{\left(x^{2} + 1\right)^{2}} + \frac{2 x + 1}{x^{2} \left(x + 1\right) \left(x^{2} + 1\right)}\right)}{x + 1}$$
The third derivative
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/ 2 \
| 4*x / 2\ / 2\ |
|-1 + ------ | (1 + 2*x) | | (1 + 2*x) | |
| 2 3*|1 - ----------| 3*(1 + 2*x)*|2 - ----------|*atan(x)|
| 1 + x 3*(1 + 2*x) \ x*(1 + x) / \ x*(1 + x) / |
2*|----------- + ----------------- - ------------------ + ------------------------------------|
| 2 2 / 2\ 2 2 |
| / 2\ / 2\ x*(1 + x)*\1 + x / x *(1 + x) |
\ \1 + x / (1 + x)*\1 + x / /
-----------------------------------------------------------------------------------------------
x*(1 + x)
$$\frac{2 \left(\frac{\frac{4 x^{2}}{x^{2} + 1} - 1}{\left(x^{2} + 1\right)^{2}} + \frac{3 \cdot \left(2 - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}\right) \left(2 x + 1\right) \operatorname{atan}{\left(x \right)}}{x^{2} \left(x + 1\right)^{2}} + \frac{3 \cdot \left(2 x + 1\right)}{\left(x + 1\right) \left(x^{2} + 1\right)^{2}} - \frac{3 \cdot \left(1 - \frac{\left(2 x + 1\right)^{2}}{x \left(x + 1\right)}\right)}{x \left(x + 1\right) \left(x^{2} + 1\right)}\right)}{x \left(x + 1\right)}$$
The graph