Sr Examen

Derivada de x*e^(x)arctanx

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
   x        
x*E *atan(x)
$$e^{x} x \operatorname{atan}{\left(x \right)}$$
(x*E^x)*atan(x)
Gráfica
Primera derivada [src]
                          x 
/ x      x\            x*e  
\E  + x*e /*atan(x) + ------
                           2
                      1 + x 
$$\frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{atan}{\left(x \right)}$$
Segunda derivada [src]
/                        2              \   
|                     2*x      2*(1 + x)|  x
|(2 + x)*atan(x) - --------- + ---------|*e 
|                          2          2 |   
|                  /     2\      1 + x  |   
\                  \1 + x /             /   
$$\left(- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{atan}{\left(x \right)}\right) e^{x}$$
Tercera derivada [src]
/                                                /         2 \\   
|                                                |      4*x  ||   
|                                            2*x*|-1 + ------||   
|                                                |          2||   
|                  3*(2 + x)   6*x*(1 + x)       \     1 + x /|  x
|(3 + x)*atan(x) + --------- - ----------- + -----------------|*e 
|                         2             2                2    |   
|                    1 + x      /     2\         /     2\     |   
\                               \1 + x /         \1 + x /     /   
$$\left(- \frac{6 x \left(x + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(x + 2\right)}{x^{2} + 1} + \left(x + 3\right) \operatorname{atan}{\left(x \right)}\right) e^{x}$$
Gráfico
Derivada de x*e^(x)arctanx