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Derivada de la función/ x^sin/ y=x^sin^x6

Derivada de y=x^sin^x6

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

Gráfico:

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Solución

Ha introducido [src] 
    x   
 sin (6)
x
xsin⁡x(6)x^{\sin^{x}{\left(6 \right)}} 
x^(sin(6)^x)
Solución detallada

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

    Perola derivada

    (log⁡(sin⁡x(6))+1)(sin⁡x(6))sin⁡x(6)\left(\log{\left(\sin^{x}{\left(6 \right)} \right)} + 1\right) \left(\sin^{x}{\left(6 \right)}\right)^{\sin^{x}{\left(6 \right)}}

Respuesta:

(log⁡(sin⁡x(6))+1)(sin⁡x(6))sin⁡x(6)\left(\log{\left(\sin^{x}{\left(6 \right)} \right)} + 1\right) \left(\sin^{x}{\left(6 \right)}\right)^{\sin^{x}{\left(6 \right)}}

Primera derivada [src] 
    x    /   x                                          \
 sin (6) |sin (6)      x                                |
x       *|------- + sin (6)*(pi*I + log(-sin(6)))*log(x)|
         \   x                                          /
xsin⁡x(6)((log⁡(−sin⁡(6))+iπ)log⁡(x)sin⁡x(6)+sin⁡x(6)x)x^{\sin^{x}{\left(6 \right)}} \left(\left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right) \log{\left(x \right)} \sin^{x}{\left(6 \right)} + \frac{\sin^{x}{\left(6 \right)}}{x}\right)
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Segunda derivada [src] 
    x            /                                         2                                                                  \
 sin (6)    x    |  1    /1                               \     x                           2          2*(pi*I + log(-sin(6)))|
x       *sin (6)*|- -- + |- + (pi*I + log(-sin(6)))*log(x)| *sin (6) + (pi*I + log(-sin(6))) *log(x) + -----------------------|
                 |   2   \x                               /                                                       x           |
                 \  x                                                                                                         /
xsin⁡x(6)(((log⁡(−sin⁡(6))+iπ)log⁡(x)+1x)2sin⁡x(6)+(log⁡(−sin⁡(6))+iπ)2log⁡(x)+2(log⁡(−sin⁡(6))+iπ)x−1x2)sin⁡x(6)x^{\sin^{x}{\left(6 \right)}} \left(\left(\left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} \sin^{x}{\left(6 \right)} + \left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right)}{x} - \frac{1}{x^{2}}\right) \sin^{x}{\left(6 \right)}
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Tercera derivada [src] 
    x            /                                       3                                                                                              2                                                                                                                \
 sin (6)    x    |2    /1                               \     2*x                           3          3*(pi*I + log(-sin(6)))   3*(pi*I + log(-sin(6)))         x    /1                               \ /  1                         2          2*(pi*I + log(-sin(6)))\|
x       *sin (6)*|-- + |- + (pi*I + log(-sin(6)))*log(x)| *sin   (6) + (pi*I + log(-sin(6))) *log(x) - ----------------------- + ------------------------ + 3*sin (6)*|- + (pi*I + log(-sin(6)))*log(x)|*|- -- + (pi*I + log(-sin(6))) *log(x) + -----------------------||
                 | 3   \x                               /                                                          2                        x                         \x                               / |   2                                              x           ||
                 \x                                                                                               x                                                                                      \  x                                                           //
xsin⁡x(6)(((log⁡(−sin⁡(6))+iπ)log⁡(x)+1x)3sin⁡2x(6)+3((log⁡(−sin⁡(6))+iπ)log⁡(x)+1x)((log⁡(−sin⁡(6))+iπ)2log⁡(x)+2(log⁡(−sin⁡(6))+iπ)x−1x2)sin⁡x(6)+(log⁡(−sin⁡(6))+iπ)3log⁡(x)+3(log⁡(−sin⁡(6))+iπ)2x−3(log⁡(−sin⁡(6))+iπ)x2+2x3)sin⁡x(6)x^{\sin^{x}{\left(6 \right)}} \left(\left(\left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} \sin^{2 x}{\left(6 \right)} + 3 \left(\left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right)}{x} - \frac{1}{x^{2}}\right) \sin^{x}{\left(6 \right)} + \left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right)^{3} \log{\left(x \right)} + \frac{3 \left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right)^{2}}{x} - \frac{3 \left(\log{\left(- \sin{\left(6 \right)} \right)} + i \pi\right)}{x^{2}} + \frac{2}{x^{3}}\right) \sin^{x}{\left(6 \right)}
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