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Derivada de la función/ tg(x)/ arctg/ xexp(-px)/arctg(x)

Derivada de xexp(-px)/arctg(x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   -p*x
x*e    
-------
atan(x)
xe−pxatan⁡(x)\frac{x e^{- p x}}{\operatorname{atan}{\left(x \right)}} 
(x*exp((-p)*x))/atan(x)
Primera derivada [src] 
       -p*x    -p*x           -p*x     
- p*x*e     + e            x*e         
------------------- - -----------------
      atan(x)         /     2\     2   
                      \1 + x /*atan (x)
−xe−px(x2+1)atan⁡2(x)+−pxe−px+e−pxatan⁡(x)- \frac{x e^{- p x}}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}} + \frac{- p x e^{- p x} + e^{- p x}}{\operatorname{atan}{\left(x \right)}}
Simplificar
Segunda derivada [src] 
/                                      /       1   \\      
|                                  2*x*|x + -------||      
|                 2*(-1 + p*x)         \    atan(x)/|  -p*x
|p*(-2 + p*x) + ---------------- + -----------------|*e    
|               /     2\                   2        |      
|               \1 + x /*atan(x)   /     2\         |      
\                                  \1 + x / *atan(x)/      
-----------------------------------------------------------
                          atan(x)
(p(px−2)+2x(x+1atan⁡(x))(x2+1)2atan⁡(x)+2(px−1)(x2+1)atan⁡(x))e−pxatan⁡(x)\frac{\left(p \left(p x - 2\right) + \frac{2 x \left(x + \frac{1}{\operatorname{atan}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{2 \left(p x - 1\right)}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}\right) e^{- p x}}{\operatorname{atan}{\left(x \right)}}
Simplificar
Tercera derivada [src] 
 /                    /                             2                    \                                                \       
 |                    |             3            4*x           6*x       |                                                |       
 |                2*x*|-1 + ----------------- + ------ + ----------------|                                   /       1   \|       
 |                    |     /     2\     2           2   /     2\        |                      6*(-1 + p*x)*|x + -------||       
 | 2                  \     \1 + x /*atan (x)   1 + x    \1 + x /*atan(x)/    3*p*(-2 + p*x)                 \    atan(x)/|  -p*x 
-|p *(-3 + p*x) + -------------------------------------------------------- + ---------------- + --------------------------|*e     
 |                                           2                               /     2\                       2             |       
 |                                   /     2\                                \1 + x /*atan(x)       /     2\              |       
 \                                   \1 + x / *atan(x)                                              \1 + x / *atan(x)     /       
----------------------------------------------------------------------------------------------------------------------------------
                                                             atan(x)
−(p2(px−3)+3p(px−2)(x2+1)atan⁡(x)+2x(4x2x2+1+6x(x2+1)atan⁡(x)−1+3(x2+1)atan⁡2(x))(x2+1)2atan⁡(x)+6(x+1atan⁡(x))(px−1)(x2+1)2atan⁡(x))e−pxatan⁡(x)- \frac{\left(p^{2} \left(p x - 3\right) + \frac{3 p \left(p x - 2\right)}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} + \frac{6 x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - 1 + \frac{3}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{6 \left(x + \frac{1}{\operatorname{atan}{\left(x \right)}}\right) \left(p x - 1\right)}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}}\right) e^{- p x}}{\operatorname{atan}{\left(x \right)}}
Simplificar
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