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- Derivative of a implicit defined function
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- Derivative of:
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Derivative of e^(5*x)
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Derivative of x^2+x+1
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Derivative of (x^2+1)^2
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Derivative of sqrt(2*x)
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Identical expressions
- ((arctan^ two)x)/ two
- ((arc tangent of squared )x) divide by 2
- ((arc tangent of to the power of two)x) divide by two
- ((arctan2)x)/2
- arctan2x/2
- ((arctan²)x)/2
- ((arctan to the power of 2)x)/2
- arctan^2x/2
- ((arctan^2)x) divide by 2
Derivative of ((arctan^2)x)/2
The solution
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[src]
2
atan (x)*x
----------
2
$$\frac{x \operatorname{atan}^{2}{\left(x \right)}}{2}$$
/ 2 \ d |atan (x)*x| --|----------| dx\ 2 /
$$\frac{d}{d x} \frac{x \operatorname{atan}^{2}{\left(x \right)}}{2}$$
The first derivative
[src]
2
atan (x) x*atan(x)
-------- + ---------
2 2
1 + x
$$\frac{\operatorname{atan}^{2}{\left(x \right)}}{2} + \frac{x \operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
The second derivative
[src]
x*(-1 + 2*x*atan(x))
2*atan(x) - --------------------
2
1 + x
--------------------------------
2
1 + x
$$\frac{- \frac{x \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{x^{2} + 1} + 2 \operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
The third derivative
[src]
/ / 2 \ \
| | 3*x 4*x *atan(x) | |
-|-3 + 2*x*|------ - ------------ + atan(x)| + 6*x*atan(x)|
| | 2 2 | |
\ \1 + x 1 + x / /
------------------------------------------------------------
2
/ 2\
\1 + x /
$$- \frac{2 x \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \operatorname{atan}{\left(x \right)} + \frac{3 x}{x^{2} + 1}\right) + 6 x \operatorname{atan}{\left(x \right)} - 3}{\left(x^{2} + 1\right)^{2}}$$
The graph