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How to use it?
- Derivative of:
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Derivative of sqrt(cos(x))
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Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of 5*tan(x)
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Derivative of (4x+1)/(3x-1)
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Identical expressions
- y=x^e^x*arctg(x)
- y equally x to the power of e to the power of x multiply by arctg(x)
- y=xex*arctg(x)
- y=xex*arctgx
- y=x^e^xarctg(x)
- y=xexarctg(x)
- y=xexarctgx
- y=x^e^xarctgx
Derivative of y=x^e^x*arctg(x)
The solution
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[src]
/ x\ \e / x *atan(x)
$$x^{e^{x}} \operatorname{atan}{\left(x \right)}$$
/ / x\ \ d | \e / | --\x *atan(x)/ dx
$$\frac{d}{d x} x^{e^{x}} \operatorname{atan}{\left(x \right)}$$
The first derivative
[src]
/ x\
\e / / x\ / x \
x \e / |e x |
------ + x *|-- + e *log(x)|*atan(x)
2 \x /
1 + x
$$x^{e^{x}} \left(e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right) \operatorname{atan}{\left(x \right)} + \frac{x^{e^{x}}}{x^{2} + 1}$$
The second derivative
[src]
/ /1 \ x\
/ x\ | / 2 \ 2*|- + log(x)|*e |
\e / | 2*x | 1 2 /1 \ x | x \x / |
x *|- --------- + |- -- + - + |- + log(x)| *e + log(x)|*atan(x)*e + -----------------|
| 2 | 2 x \x / | 2 |
| / 2\ \ x / 1 + x |
\ \1 + x / /
$$x^{e^{x}} \left(- \frac{2 x}{\left(x^{2} + 1\right)^{2}} + \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} + \log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x} \operatorname{atan}{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x}}{x^{2} + 1}\right)$$
The third derivative
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/ / 2 \ / 2 \ \
| | 4*x | | 1 2 /1 \ x | x |
|2*|-1 + ------| 3*|- -- + - + |- + log(x)| *e + log(x)|*e /1 \ x|
/ x\ | | 2| / 3 \ | 2 x \x / | 6*x*|- + log(x)|*e |
\e / | \ 1 + x / | 3 2 3 /1 \ 2*x /1 \ / 1 2 \ x | x \ x / \x / |
x *|--------------- + |- -- + -- + - + |- + log(x)| *e + 3*|- + log(x)|*|- -- + - + log(x)|*e + log(x)|*atan(x)*e + ------------------------------------------- - -------------------|
| 2 | 2 3 x \x / \x / | 2 x | | 2 2 |
| / 2\ \ x x \ x / / 1 + x / 2\ |
\ \1 + x / \1 + x / /
$$x^{e^{x}} \left(- \frac{6 x \left(\log{\left(x \right)} + \frac{1}{x}\right) e^{x}}{\left(x^{2} + 1\right)^{2}} + \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 x} + 3 \left(\log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x} + \log{\left(x \right)} + \frac{3}{x} - \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) e^{x} \operatorname{atan}{\left(x \right)} + \frac{3 \left(\left(\log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x} + \log{\left(x \right)} + \frac{2}{x} - \frac{1}{x^{2}}\right) e^{x}}{x^{2} + 1} + \frac{2 \cdot \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}\right)$$
The graph