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y=(sin(x))^(5*exp(x))
Derivada de la función/ sin(x)/ exp(x)/ y=(sin(x))^(5*exp(x))

Derivada de y=(sin(x))^(5*exp(x))

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

Ha introducido [src] 
           x
        5*e 
(sin(x))
sin⁡5ex(x)\sin^{5 e^{x}}{\left(x \right)} 
sin(x)^(5*exp(x))
Solución detallada

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

    Perola derivada

    (5ex)5ex(log⁡(5ex)+1)\left(5 e^{x}\right)^{5 e^{x}} \left(\log{\left(5 e^{x} \right)} + 1\right)

  2. Simplificamos:

    (3125e5x)ex(x+1+log⁡(5))\left(3125 e^{5 x}\right)^{e^{x}} \left(x + 1 + \log{\left(5 \right)}\right)

Respuesta:

(3125e5x)ex(x+1+log⁡(5))\left(3125 e^{5 x}\right)^{e^{x}} \left(x + 1 + \log{\left(5 \right)}\right)

Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
           x /                             x\
        5*e  |   x               5*cos(x)*e |
(sin(x))    *|5*e *log(sin(x)) + -----------|
             \                      sin(x)  /
(5exlog⁡(sin⁡(x))+5excos⁡(x)sin⁡(x))sin⁡5ex(x)\left(5 e^{x} \log{\left(\sin{\left(x \right)} \right)} + \frac{5 e^{x} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{5 e^{x}}{\left(x \right)}
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Segunda derivada [src] 
             x /        2                                         2                 \   
          5*e  |     cos (x)   2*cos(x)     /cos(x)              \   x              |  x
5*(sin(x))    *|-1 - ------- + -------- + 5*|------ + log(sin(x))| *e  + log(sin(x))|*e 
               |        2       sin(x)      \sin(x)              /                  |   
               \     sin (x)                                                        /
5(5(log⁡(sin⁡(x))+cos⁡(x)sin⁡(x))2ex+log⁡(sin⁡(x))−1+2cos⁡(x)sin⁡(x)−cos⁡2(x)sin⁡2(x))exsin⁡5ex(x)5 \left(5 \left(\log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} e^{x} + \log{\left(\sin{\left(x \right)} \right)} - 1 + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) e^{x} \sin^{5 e^{x}}{\left(x \right)}
Simplificar
Tercera derivada [src] 
             x /          2           3                                          3                                  /        2                            \                 \   
          5*e  |     3*cos (x)   2*cos (x)   5*cos(x)      /cos(x)              \   2*x      /cos(x)              \ |     cos (x)   2*cos(x)              |  x              |  x
5*(sin(x))    *|-3 - --------- + --------- + -------- + 25*|------ + log(sin(x))| *e    + 15*|------ + log(sin(x))|*|-1 - ------- + -------- + log(sin(x))|*e  + log(sin(x))|*e 
               |         2           3        sin(x)       \sin(x)              /            \sin(x)              / |        2       sin(x)               |                 |   
               \      sin (x)     sin (x)                                                                           \     sin (x)                         /                 /
5(25(log⁡(sin⁡(x))+cos⁡(x)sin⁡(x))3e2x+15(log⁡(sin⁡(x))+cos⁡(x)sin⁡(x))(log⁡(sin⁡(x))−1+2cos⁡(x)sin⁡(x)−cos⁡2(x)sin⁡2(x))ex+log⁡(sin⁡(x))−3+5cos⁡(x)sin⁡(x)−3cos⁡2(x)sin⁡2(x)+2cos⁡3(x)sin⁡3(x))exsin⁡5ex(x)5 \left(25 \left(\log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} e^{2 x} + 15 \left(\log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\log{\left(\sin{\left(x \right)} \right)} - 1 + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) e^{x} + \log{\left(\sin{\left(x \right)} \right)} - 3 + \frac{5 \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) e^{x} \sin^{5 e^{x}}{\left(x \right)}
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Gráfico
Derivada de y=(sin(x))^(5*exp(x))
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