Sr Examen

Derivada de xex

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
 / x\
 \E /
x    
xexx^{e^{x}}
x^(E^x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log(ex)+1)exex\left(\log{\left(e^{x} \right)} + 1\right) e^{x e^{x}}

  2. Simplificamos:

    (x+1)exex\left(x + 1\right) e^{x e^{x}}


Respuesta:

(x+1)exex\left(x + 1\right) e^{x e^{x}}

Primera derivada [src]
 / x\ / x            \
 \E / |e     x       |
x    *|-- + e *log(x)|
      \x             /
xex(exlog(x)+exx)x^{e^{x}} \left(e^{x} \log{\left(x \right)} + \frac{e^{x}}{x}\right)
Segunda derivada [src]
 / x\ /                       2            \   
 \e / |  1    2   /1         \   x         |  x
x    *|- -- + - + |- + log(x)| *e  + log(x)|*e 
      |   2   x   \x         /             |   
      \  x                                 /   
xex((log(x)+1x)2ex+log(x)+2x1x2)exx^{e^{x}} \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}
Tercera derivada [src]
 / x\ /                            3                                                      \   
 \e / |  3    2    3   /1         \   2*x     /1         \ /  1    2         \  x         |  x
x    *|- -- + -- + - + |- + log(x)| *e    + 3*|- + log(x)|*|- -- + - + log(x)|*e  + log(x)|*e 
      |   2    3   x   \x         /           \x         / |   2   x         |            |   
      \  x    x                                            \  x              /            /   
xex((log(x)+1x)3e2x+3(log(x)+1x)(log(x)+2x1x2)ex+log(x)+3x3x2+2x3)exx^{e^{x}} \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}