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Derivada de la función/ x^sin/ sine^x/ x^sine^x

Derivada de x^sine^x

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

Gráfico:

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Definida a trozos:

Solución

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

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

    Perola derivada

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

  2. Simplificamos:

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

Respuesta:

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

Primera derivada [src] 
    x    /   x                                \
 sin (E) |sin (E)      x                      |
x       *|------- + sin (E)*log(x)*log(sin(E))|
         \   x                                /
xsin⁡x(e)(log⁡(x)log⁡(sin⁡(e))sin⁡x(e)+sin⁡x(e)x)x^{\sin^{x}{\left(e \right)}} \left(\log{\left(x \right)} \log{\left(\sin{\left(e \right)} \right)} \sin^{x}{\left(e \right)} + \frac{\sin^{x}{\left(e \right)}}{x}\right)
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Segunda derivada [src] 
    x            /                               2                                              \
 sin (E)    x    |  1    /1                     \     x         2                  2*log(sin(E))|
x       *sin (E)*|- -- + |- + log(x)*log(sin(E))| *sin (E) + log (sin(E))*log(x) + -------------|
                 |   2   \x                     /                                        x      |
                 \  x                                                                           /
xsin⁡x(e)((log⁡(x)log⁡(sin⁡(e))+1x)2sin⁡x(e)+log⁡(x)log⁡(sin⁡(e))2+2log⁡(sin⁡(e))x−1x2)sin⁡x(e)x^{\sin^{x}{\left(e \right)}} \left(\left(\log{\left(x \right)} \log{\left(\sin{\left(e \right)} \right)} + \frac{1}{x}\right)^{2} \sin^{x}{\left(e \right)} + \log{\left(x \right)} \log{\left(\sin{\left(e \right)} \right)}^{2} + \frac{2 \log{\left(\sin{\left(e \right)} \right)}}{x} - \frac{1}{x^{2}}\right) \sin^{x}{\left(e \right)}
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Tercera derivada [src] 
    x            /                             3                                                        2                                                                                          \
 sin (E)    x    |2    /1                     \     2*x         3                  3*log(sin(E))   3*log (sin(E))        x    /1                     \ /  1       2                  2*log(sin(E))\|
x       *sin (E)*|-- + |- + log(x)*log(sin(E))| *sin   (E) + log (sin(E))*log(x) - ------------- + -------------- + 3*sin (E)*|- + log(x)*log(sin(E))|*|- -- + log (sin(E))*log(x) + -------------||
                 | 3   \x                     /                                           2              x                    \x                     / |   2                               x      ||
                 \x                                                                      x                                                             \  x                                       //
xsin⁡x(e)((log⁡(x)log⁡(sin⁡(e))+1x)3sin⁡2x(e)+3(log⁡(x)log⁡(sin⁡(e))+1x)(log⁡(x)log⁡(sin⁡(e))2+2log⁡(sin⁡(e))x−1x2)sin⁡x(e)+log⁡(x)log⁡(sin⁡(e))3+3log⁡(sin⁡(e))2x−3log⁡(sin⁡(e))x2+2x3)sin⁡x(e)x^{\sin^{x}{\left(e \right)}} \left(\left(\log{\left(x \right)} \log{\left(\sin{\left(e \right)} \right)} + \frac{1}{x}\right)^{3} \sin^{2 x}{\left(e \right)} + 3 \left(\log{\left(x \right)} \log{\left(\sin{\left(e \right)} \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} \log{\left(\sin{\left(e \right)} \right)}^{2} + \frac{2 \log{\left(\sin{\left(e \right)} \right)}}{x} - \frac{1}{x^{2}}\right) \sin^{x}{\left(e \right)} + \log{\left(x \right)} \log{\left(\sin{\left(e \right)} \right)}^{3} + \frac{3 \log{\left(\sin{\left(e \right)} \right)}^{2}}{x} - \frac{3 \log{\left(\sin{\left(e \right)} \right)}}{x^{2}} + \frac{2}{x^{3}}\right) \sin^{x}{\left(e \right)}
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