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x*(x^2+1)*arctgxexp(-x)
Derivada de la función/ x^2+1/ arctg/ exp(-x)/ x*(x^2+1)*arctgxexp(-x)

Derivada de x*(x^2+1)*arctgxexp(-x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
  / 2    \          -x
x*\x  + 1/*acot(x)*e
x(x2+1)acot⁡(x)e−xx \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)} e^{- x} 
((x*(x^2 + 1))*acot(x))*exp(-x)
Gráfica
02468-8-6-4-2-1010-50000005000000
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Primera derivada [src] 
/                       / 2    \\                             
|/       2\           x*\x  + 1/|  -x     / 2    \          -x
|\1 + 3*x /*acot(x) - ----------|*e   - x*\x  + 1/*acot(x)*e  
|                            2  |                             
\                       1 + x   /
−x(x2+1)e−xacot⁡(x)+(−x(x2+1)x2+1+(3x2+1)acot⁡(x))e−x- x \left(x^{2} + 1\right) e^{- x} \operatorname{acot}{\left(x \right)} + \left(- \frac{x \left(x^{2} + 1\right)}{x^{2} + 1} + \left(3 x^{2} + 1\right) \operatorname{acot}{\left(x \right)}\right) e^{- x}
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Segunda derivada [src] 
/        /       2\                              2                                    \    
|      2*\1 + 3*x /     /       2\            2*x                     /     2\        |  -x
|2*x - ------------ - 2*\1 + 3*x /*acot(x) + ------ + 6*x*acot(x) + x*\1 + x /*acot(x)|*e  
|              2                                  2                                   |    
\         1 + x                              1 + x                                    /
(2x2x2+1+x(x2+1)acot⁡(x)+6xacot⁡(x)+2x−2(3x2+1)acot⁡(x)−2(3x2+1)x2+1)e−x\left(\frac{2 x^{2}}{x^{2} + 1} + x \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)} + 6 x \operatorname{acot}{\left(x \right)} + 2 x - 2 \left(3 x^{2} + 1\right) \operatorname{acot}{\left(x \right)} - \frac{2 \left(3 x^{2} + 1\right)}{x^{2} + 1}\right) e^{- x}
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Tercera derivada [src] 
 /                                                                                                                                    /         2 \\    
 |                                                                                                                                    |      4*x  ||    
 |                                                                                                                                2*x*|-1 + ------||    
 |                     /       2\                              2                                                     /       2\       |          2||    
 |                   6*\1 + 3*x /     /       2\            6*x      18*x                     /     2\           6*x*\1 + 3*x /       \     1 + x /|  -x
-|-6*acot(x) + 3*x - ------------ - 3*\1 + 3*x /*acot(x) + ------ + ------ + 18*x*acot(x) + x*\1 + x /*acot(x) - -------------- + -----------------|*e  
 |                           2                                  2        2                                                 2                 2     |    
 |                      1 + x                              1 + x    1 + x                                          /     2\             1 + x      |    
 \                                                                                                                 \1 + x /                        /
−(6x2x2+1+x(x2+1)acot⁡(x)+18xacot⁡(x)+3x+2x(4x2x2+1−1)x2+1+18xx2+1−6x(3x2+1)(x2+1)2−3(3x2+1)acot⁡(x)−6acot⁡(x)−6(3x2+1)x2+1)e−x- \left(\frac{6 x^{2}}{x^{2} + 1} + x \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)} + 18 x \operatorname{acot}{\left(x \right)} + 3 x + \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + \frac{18 x}{x^{2} + 1} - \frac{6 x \left(3 x^{2} + 1\right)}{\left(x^{2} + 1\right)^{2}} - 3 \left(3 x^{2} + 1\right) \operatorname{acot}{\left(x \right)} - 6 \operatorname{acot}{\left(x \right)} - \frac{6 \left(3 x^{2} + 1\right)}{x^{2} + 1}\right) e^{- x}
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Gráfico
Derivada de x*(x^2+1)*arctgxexp(-x)
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