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Derivada de la función/ x*exp/ exp(x)/ x^(x*exp(x))

Derivada de x^(x*exp(x))

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

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Solución

Ha introducido [src] 
    x
 x*e 
x
xxexx^{x e^{x}} 
x^(x*exp(x))
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (xex)xex(log⁡(xex)+1)\left(x e^{x}\right)^{x e^{x}} \left(\log{\left(x e^{x} \right)} + 1\right)

  2. Simplificamos:

    (xex)xex(x+log⁡(x)+1)\left(x e^{x}\right)^{x e^{x}} \left(x + \log{\left(x \right)} + 1\right)

Respuesta:

(xex)xex(x+log⁡(x)+1)\left(x e^{x}\right)^{x e^{x}} \left(x + \log{\left(x \right)} + 1\right)

Primera derivada [src] 
    x                          
 x*e  //   x    x\           x\
x    *\\x*e  + e /*log(x) + e /
xxex((xex+ex)log⁡(x)+ex)x^{x e^{x}} \left(\left(x e^{x} + e^{x}\right) \log{\left(x \right)} + e^{x}\right)
Simplificar
Segunda derivada [src] 
    x                                                           
 x*e  /    1 + x                       2  x                 \  x
x    *|1 + ----- + (1 + (1 + x)*log(x)) *e  + (2 + x)*log(x)|*e 
      \      x                                              /
xxex((x+2)log⁡(x)+((x+1)log⁡(x)+1)2ex+1+x+1x)exx^{x e^{x}} \left(\left(x + 2\right) \log{\left(x \right)} + \left(\left(x + 1\right) \log{\left(x \right)} + 1\right)^{2} e^{x} + 1 + \frac{x + 1}{x}\right) e^{x}
Simplificar
Tercera derivada [src] 
    x                                                                                                                                  
 x*e  /                        3  2*x                    1 + x   2*(2 + x)                          /    1 + x                 \  x\  x
x    *|1 + (1 + (1 + x)*log(x)) *e    + (3 + x)*log(x) - ----- + --------- + 3*(1 + (1 + x)*log(x))*|1 + ----- + (2 + x)*log(x)|*e |*e 
      |                                                     2        x                              \      x                   /   |   
      \                                                    x                                                                       /
xxex((x+3)log⁡(x)+((x+1)log⁡(x)+1)3e2x+3((x+1)log⁡(x)+1)((x+2)log⁡(x)+1+x+1x)ex+1+2(x+2)x−x+1x2)exx^{x e^{x}} \left(\left(x + 3\right) \log{\left(x \right)} + \left(\left(x + 1\right) \log{\left(x \right)} + 1\right)^{3} e^{2 x} + 3 \left(\left(x + 1\right) \log{\left(x \right)} + 1\right) \left(\left(x + 2\right) \log{\left(x \right)} + 1 + \frac{x + 1}{x}\right) e^{x} + 1 + \frac{2 \left(x + 2\right)}{x} - \frac{x + 1}{x^{2}}\right) e^{x}
Simplificar
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