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(x+sin(x-e))^lne^x
Derivada de la función/ x+sin/ lne^x/ (x+sin(x-e))^lne^x

Derivada de (x+sin(x-e))^lne^x

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

Gráfico:

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Solución

Ha introducido [src] 
                   x   
                log (E)
(x + sin(x - E))
(x+sin⁡(x−e))log⁡(e)x\left(x + \sin{\left(x - e \right)}\right)^{\log{\left(e \right)}^{x}} 
(x + sin(x - E))^(log(E)^x)
Solución detallada

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

    Perola derivada

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

  2. Simplificamos:

    11

Respuesta:

11

Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                   x    /   x                                                              \
                log (E) |log (E)*(1 + cos(x - E))      x                                   |
(x + sin(x - E))       *|------------------------ + log (E)*log(x + sin(x - E))*log(log(E))|
                        \     x + sin(x - E)                                               /
(x+sin⁡(x−e))log⁡(e)x(log⁡(e)xlog⁡(x+sin⁡(x−e))log⁡(log⁡(e))+(cos⁡(x−e)+1)log⁡(e)xx+sin⁡(x−e))\left(x + \sin{\left(x - e \right)}\right)^{\log{\left(e \right)}^{x}} \left(\log{\left(e \right)}^{x} \log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)} + \frac{\left(\cos{\left(x - e \right)} + 1\right) \log{\left(e \right)}^{x}}{x + \sin{\left(x - e \right)}}\right)
Simplificar
Segunda derivada [src] 
                   x            /                                                  2                                                              2                                                  \
                log (E)    x    |/1 + cos(x - E)                                  \     x         2                               (1 + cos(x - E))      sin(x - E)     2*(1 + cos(x - E))*log(log(E))|
(x + sin(x - E))       *log (E)*||-------------- + log(x + sin(x - E))*log(log(E))| *log (E) + log (log(E))*log(x + sin(x - E)) - ----------------- - -------------- + ------------------------------|
                                |\x + sin(x - E)                                  /                                                               2   x + sin(x - E)           x + sin(x - E)        |
                                \                                                                                                 (x + sin(x - E))                                                   /
(x+sin⁡(x−e))log⁡(e)x((log⁡(x+sin⁡(x−e))log⁡(log⁡(e))+cos⁡(x−e)+1x+sin⁡(x−e))2log⁡(e)x+log⁡(x+sin⁡(x−e))log⁡(log⁡(e))2+2(cos⁡(x−e)+1)log⁡(log⁡(e))x+sin⁡(x−e)−sin⁡(x−e)x+sin⁡(x−e)−(cos⁡(x−e)+1)2(x+sin⁡(x−e))2)log⁡(e)x\left(x + \sin{\left(x - e \right)}\right)^{\log{\left(e \right)}^{x}} \left(\left(\log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)} + \frac{\cos{\left(x - e \right)} + 1}{x + \sin{\left(x - e \right)}}\right)^{2} \log{\left(e \right)}^{x} + \log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)}^{2} + \frac{2 \left(\cos{\left(x - e \right)} + 1\right) \log{\left(\log{\left(e \right)} \right)}}{x + \sin{\left(x - e \right)}} - \frac{\sin{\left(x - e \right)}}{x + \sin{\left(x - e \right)}} - \frac{\left(\cos{\left(x - e \right)} + 1\right)^{2}}{\left(x + \sin{\left(x - e \right)}\right)^{2}}\right) \log{\left(e \right)}^{x}
Simplificar
Tercera derivada [src] 
                   x            /                                                  3                                                                                   3                     2                                               2                                                                                                                         /                                                   2                                                  \\
                log (E)    x    |/1 + cos(x - E)                                  \     2*x         3                                 cos(x - E)     2*(1 + cos(x - E))    3*(1 + cos(x - E)) *log(log(E))   3*log(log(E))*sin(x - E)   3*log (log(E))*(1 + cos(x - E))   3*(1 + cos(x - E))*sin(x - E)        x    /1 + cos(x - E)                                  \ |   2                               (1 + cos(x - E))      sin(x - E)     2*(1 + cos(x - E))*log(log(E))||
(x + sin(x - E))       *log (E)*||-------------- + log(x + sin(x - E))*log(log(E))| *log   (E) + log (log(E))*log(x + sin(x - E)) - -------------- + ------------------- - ------------------------------- - ------------------------ + ------------------------------- + ----------------------------- + 3*log (E)*|-------------- + log(x + sin(x - E))*log(log(E))|*|log (log(E))*log(x + sin(x - E)) - ----------------- - -------------- + ------------------------------||
                                |\x + sin(x - E)                                  /                                                 x + sin(x - E)                    3                           2               x + sin(x - E)                 x + sin(x - E)                                 2                   \x + sin(x - E)                                  / |                                                   2   x + sin(x - E)           x + sin(x - E)        ||
                                \                                                                                                                     (x + sin(x - E))            (x + sin(x - E))                                                                              (x + sin(x - E))                                                                       \                                   (x + sin(x - E))                                                   //
(x+sin⁡(x−e))log⁡(e)x((log⁡(x+sin⁡(x−e))log⁡(log⁡(e))+cos⁡(x−e)+1x+sin⁡(x−e))3log⁡(e)2x+3(log⁡(x+sin⁡(x−e))log⁡(log⁡(e))+cos⁡(x−e)+1x+sin⁡(x−e))(log⁡(x+sin⁡(x−e))log⁡(log⁡(e))2+2(cos⁡(x−e)+1)log⁡(log⁡(e))x+sin⁡(x−e)−sin⁡(x−e)x+sin⁡(x−e)−(cos⁡(x−e)+1)2(x+sin⁡(x−e))2)log⁡(e)x+log⁡(x+sin⁡(x−e))log⁡(log⁡(e))3+3(cos⁡(x−e)+1)log⁡(log⁡(e))2x+sin⁡(x−e)−3log⁡(log⁡(e))sin⁡(x−e)x+sin⁡(x−e)−cos⁡(x−e)x+sin⁡(x−e)−3(cos⁡(x−e)+1)2log⁡(log⁡(e))(x+sin⁡(x−e))2+3(cos⁡(x−e)+1)sin⁡(x−e)(x+sin⁡(x−e))2+2(cos⁡(x−e)+1)3(x+sin⁡(x−e))3)log⁡(e)x\left(x + \sin{\left(x - e \right)}\right)^{\log{\left(e \right)}^{x}} \left(\left(\log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)} + \frac{\cos{\left(x - e \right)} + 1}{x + \sin{\left(x - e \right)}}\right)^{3} \log{\left(e \right)}^{2 x} + 3 \left(\log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)} + \frac{\cos{\left(x - e \right)} + 1}{x + \sin{\left(x - e \right)}}\right) \left(\log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)}^{2} + \frac{2 \left(\cos{\left(x - e \right)} + 1\right) \log{\left(\log{\left(e \right)} \right)}}{x + \sin{\left(x - e \right)}} - \frac{\sin{\left(x - e \right)}}{x + \sin{\left(x - e \right)}} - \frac{\left(\cos{\left(x - e \right)} + 1\right)^{2}}{\left(x + \sin{\left(x - e \right)}\right)^{2}}\right) \log{\left(e \right)}^{x} + \log{\left(x + \sin{\left(x - e \right)} \right)} \log{\left(\log{\left(e \right)} \right)}^{3} + \frac{3 \left(\cos{\left(x - e \right)} + 1\right) \log{\left(\log{\left(e \right)} \right)}^{2}}{x + \sin{\left(x - e \right)}} - \frac{3 \log{\left(\log{\left(e \right)} \right)} \sin{\left(x - e \right)}}{x + \sin{\left(x - e \right)}} - \frac{\cos{\left(x - e \right)}}{x + \sin{\left(x - e \right)}} - \frac{3 \left(\cos{\left(x - e \right)} + 1\right)^{2} \log{\left(\log{\left(e \right)} \right)}}{\left(x + \sin{\left(x - e \right)}\right)^{2}} + \frac{3 \left(\cos{\left(x - e \right)} + 1\right) \sin{\left(x - e \right)}}{\left(x + \sin{\left(x - e \right)}\right)^{2}} + \frac{2 \left(\cos{\left(x - e \right)} + 1\right)^{3}}{\left(x + \sin{\left(x - e \right)}\right)^{3}}\right) \log{\left(e \right)}^{x}
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Gráfico
Derivada de (x+sin(x-e))^lne^x
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