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How to use it?
- Derivative of:
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Derivative of (1+x)/(4-x^2)
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Derivative of (1+sqrt(x))/(1-sqrt(x))
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Derivative of y=x^3×cosx
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Derivative of (2*x-1)/(x-1)^2
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Identical expressions
- x*arctg(x)ctg(x)*cos(x)
- x multiply by arctg(x)ctg(x) multiply by co sinus of e of (x)
- xarctg(x)ctg(x)cos(x)
- xarctgxctgxcosx
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Similar expressions
- x*arctg(x)ctg(x)*cosx
Derivative of x*arctg(x)ctg(x)*cos(x)
The solution
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[src]
x*atan(x)*cot(x)*cos(x)
$$x \operatorname{atan}{\left(x \right)} \cot{\left(x \right)} \cos{\left(x \right)}$$
((x*atan(x))*cot(x))*cos(x)
The first derivative
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// x \ / 2 \ \ ||------ + atan(x)|*cot(x) + x*\-1 - cot (x)/*atan(x)|*cos(x) - x*atan(x)*cot(x)*sin(x) || 2 | | \\1 + x / /
$$- x \sin{\left(x \right)} \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + \left(x \left(- \cot^{2}{\left(x \right)} - 1\right) \operatorname{atan}{\left(x \right)} + \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \cot{\left(x \right)}\right) \cos{\left(x \right)}$$
The second derivative
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/ / 2 \ \
| | x | |
| |-1 + ------|*cot(x) |
| | 2| |
|/ 2 \ / x \ \ 1 + x / / 2 \ | / / x \ / 2 \ \
- 2*|\1 + cot (x)/*|------ + atan(x)| + -------------------- - x*\1 + cot (x)/*atan(x)*cot(x)|*cos(x) + 2*|- |------ + atan(x)|*cot(x) + x*\1 + cot (x)/*atan(x)|*sin(x) - x*atan(x)*cos(x)*cot(x)
| | 2 | 2 | | | 2 | |
\ \1 + x / 1 + x / \ \1 + x / /
$$- x \cos{\left(x \right)} \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + 2 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} - \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \cot{\left(x \right)}\right) \sin{\left(x \right)} - 2 \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) + \frac{\left(\frac{x^{2}}{x^{2} + 1} - 1\right) \cot{\left(x \right)}}{x^{2} + 1}\right) \cos{\left(x \right)}$$
The third derivative
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/ / 2 \ / 2 \ \ / / 2 \ \ | / 2 \ | x | | x | | | | x | | |3*\1 + cot (x)/*|-1 + ------| 4*x*|-1 + ------|*cot(x)| | |-1 + ------|*cot(x) | | | 2| | 2| | | | 2| | | \ 1 + x / / 2 \ / x \ / 2 \ / 2 \ \ 1 + x / | / / x \ / 2 \ \ |/ 2 \ / x \ \ 1 + x / / 2 \ | 2*|----------------------------- + 3*\1 + cot (x)/*|------ + atan(x)|*cot(x) - x*\1 + cot (x)/*\1 + 3*cot (x)/*atan(x) + ------------------------|*cos(x) + 3*|- |------ + atan(x)|*cot(x) + x*\1 + cot (x)/*atan(x)|*cos(x) + 6*|\1 + cot (x)/*|------ + atan(x)| + -------------------- - x*\1 + cot (x)/*atan(x)*cot(x)|*sin(x) + x*atan(x)*cot(x)*sin(x) | 2 | 2 | 2 | | | 2 | | | | 2 | 2 | | 1 + x \1 + x / / 2\ | \ \1 + x / / \ \1 + x / 1 + x / \ \1 + x / /
$$x \sin{\left(x \right)} \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + 3 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} - \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \cot{\left(x \right)}\right) \cos{\left(x \right)} + 6 \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) + \frac{\left(\frac{x^{2}}{x^{2} + 1} - 1\right) \cot{\left(x \right)}}{x^{2} + 1}\right) \sin{\left(x \right)} + 2 \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} + \frac{4 x \left(\frac{x^{2}}{x^{2} + 1} - 1\right) \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + 3 \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + \frac{3 \left(\frac{x^{2}}{x^{2} + 1} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{2} + 1}\right) \cos{\left(x \right)}$$