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Derivada de la función/ tan(x)/ x^(e^(-tan(x))*x)

Derivada de x^(e^(-tan(x))*x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
  -tan(x)  
 E       *x
x
xe−tan⁡(x)xx^{e^{- \tan{\left(x \right)}} x} 
x^(E^(-tan(x))*x)
Solución detallada

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

    Perola derivada

    (e−tan⁡(x)x)e−tan⁡(x)x(log⁡(e−tan⁡(x)x)+1)\left(e^{- \tan{\left(x \right)}} x\right)^{e^{- \tan{\left(x \right)}} x} \left(\log{\left(e^{- \tan{\left(x \right)}} x \right)} + 1\right)

  2. Simplificamos:

    xxe−tan⁡(x)(log⁡(xe−tan⁡(x))+1)e−xe−tan⁡(x)tan⁡(x)x^{x e^{- \tan{\left(x \right)}}} \left(\log{\left(x e^{- \tan{\left(x \right)}} \right)} + 1\right) e^{- x e^{- \tan{\left(x \right)}} \tan{\left(x \right)}}

Respuesta:

xxe−tan⁡(x)(log⁡(xe−tan⁡(x))+1)e−xe−tan⁡(x)tan⁡(x)x^{x e^{- \tan{\left(x \right)}}} \left(\log{\left(x e^{- \tan{\left(x \right)}} \right)} + 1\right) e^{- x e^{- \tan{\left(x \right)}} \tan{\left(x \right)}}

Primera derivada [src] 
  -tan(x)                                                             
 E       *x // -tan(x)     /        2   \  -tan(x)\           -tan(x)\
x          *\\E        + x*\-1 - tan (x)/*e       /*log(x) + e       /
xe−tan⁡(x)x((x(−tan⁡2(x)−1)e−tan⁡(x)+e−tan⁡(x))log⁡(x)+e−tan⁡(x))x^{e^{- \tan{\left(x \right)}} x} \left(\left(x \left(- \tan^{2}{\left(x \right)} - 1\right) e^{- \tan{\left(x \right)}} + e^{- \tan{\left(x \right)}}\right) \log{\left(x \right)} + e^{- \tan{\left(x \right)}}\right)
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Segunda derivada [src] 
    -tan(x) /                                                   2                   /       2   \                                                          \         
 x*e        |        2      /     /       /       2   \\       \   -tan(x)   -1 + x*\1 + tan (x)/   /       2   \ /      /       2   \             \       |  -tan(x)
x          *|-1 - tan (x) + \-1 + \-1 + x*\1 + tan (x)//*log(x)/ *e        - -------------------- - \1 + tan (x)/*\2 - x*\1 + tan (x)/ + 2*x*tan(x)/*log(x)|*e       
            \                                                                         x                                                                    /
xxe−tan⁡(x)(((x(tan⁡2(x)+1)−1)log⁡(x)−1)2e−tan⁡(x)−(tan⁡2(x)+1)(−x(tan⁡2(x)+1)+2xtan⁡(x)+2)log⁡(x)−tan⁡2(x)−1−x(tan⁡2(x)+1)−1x)e−tan⁡(x)x^{x e^{- \tan{\left(x \right)}}} \left(\left(\left(x \left(\tan^{2}{\left(x \right)} + 1\right) - 1\right) \log{\left(x \right)} - 1\right)^{2} e^{- \tan{\left(x \right)}} - \left(\tan^{2}{\left(x \right)} + 1\right) \left(- x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 x \tan{\left(x \right)} + 2\right) \log{\left(x \right)} - \tan^{2}{\left(x \right)} - 1 - \frac{x \left(\tan^{2}{\left(x \right)} + 1\right) - 1}{x}\right) e^{- \tan{\left(x \right)}}
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Tercera derivada [src] 
    -tan(x) /             2          /       2   \                                       3                                                     /                                           2                                                             \            /       2   \ /      /       2   \             \                                          /                     /       2   \                                                          \         \         
 x*e        |/       2   \    -1 + x*\1 + tan (x)/   /     /       /       2   \\       \   -2*tan(x)     /       2   \          /       2   \ |          2                   /       2   \        /       2   \          2          /       2   \       |          2*\1 + tan (x)/*\2 - x*\1 + tan (x)/ + 2*x*tan(x)/     /     /       /       2   \\       \ |       2      -1 + x*\1 + tan (x)/   /       2   \ /      /       2   \             \       |  -tan(x)|  -tan(x)
x          *|\1 + tan (x)/  + -------------------- - \-1 + \-1 + x*\1 + tan (x)//*log(x)/ *e          - 2*\1 + tan (x)/*tan(x) - \1 + tan (x)/*\-3 - 3*tan (x) + 6*tan(x) + x*\1 + tan (x)/  + 2*x*\1 + tan (x)/ + 4*x*tan (x) - 6*x*\1 + tan (x)/*tan(x)/*log(x) - -------------------------------------------------- + 3*\-1 + \-1 + x*\1 + tan (x)//*log(x)/*|1 + tan (x) + -------------------- + \1 + tan (x)/*\2 - x*\1 + tan (x)/ + 2*x*tan(x)/*log(x)|*e       |*e       
            |                           2                                                                                                                                                                                                                                                   x                                                                   \                       x                                                                    /         |         
            \                          x                                                                                                                                                                                                                                                                                                                                                                                                                               /
xxe−tan⁡(x)(−((x(tan⁡2(x)+1)−1)log⁡(x)−1)3e−2tan⁡(x)+3((x(tan⁡2(x)+1)−1)log⁡(x)−1)((tan⁡2(x)+1)(−x(tan⁡2(x)+1)+2xtan⁡(x)+2)log⁡(x)+tan⁡2(x)+1+x(tan⁡2(x)+1)−1x)e−tan⁡(x)+(tan⁡2(x)+1)2−(tan⁡2(x)+1)(x(tan⁡2(x)+1)2−6x(tan⁡2(x)+1)tan⁡(x)+2x(tan⁡2(x)+1)+4xtan⁡2(x)−3tan⁡2(x)+6tan⁡(x)−3)log⁡(x)−2(tan⁡2(x)+1)tan⁡(x)−2(tan⁡2(x)+1)(−x(tan⁡2(x)+1)+2xtan⁡(x)+2)x+x(tan⁡2(x)+1)−1x2)e−tan⁡(x)x^{x e^{- \tan{\left(x \right)}}} \left(- \left(\left(x \left(\tan^{2}{\left(x \right)} + 1\right) - 1\right) \log{\left(x \right)} - 1\right)^{3} e^{- 2 \tan{\left(x \right)}} + 3 \left(\left(x \left(\tan^{2}{\left(x \right)} + 1\right) - 1\right) \log{\left(x \right)} - 1\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(- x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 x \tan{\left(x \right)} + 2\right) \log{\left(x \right)} + \tan^{2}{\left(x \right)} + 1 + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right) - 1}{x}\right) e^{- \tan{\left(x \right)}} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} - \left(\tan^{2}{\left(x \right)} + 1\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right)^{2} - 6 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 2 x \left(\tan^{2}{\left(x \right)} + 1\right) + 4 x \tan^{2}{\left(x \right)} - 3 \tan^{2}{\left(x \right)} + 6 \tan{\left(x \right)} - 3\right) \log{\left(x \right)} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- x \left(\tan^{2}{\left(x \right)} + 1\right) + 2 x \tan{\left(x \right)} + 2\right)}{x} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right) - 1}{x^{2}}\right) e^{- \tan{\left(x \right)}}
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