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y=(sinx)^x^cosx
Derivada de la función/ x^cosx/ (sinx)/ y=(sinx)^x^cosx

Derivada de y=(sinx)^x^cosx

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
        / cos(x)\
        \x      /
(sin(x))
sin⁡xcos⁡(x)(x)\sin^{x^{\cos{\left(x \right)}}}{\left(x \right)} 
sin(x)^(x^cos(x))
Solución detallada

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

    Perola derivada

    (log⁡(xcos⁡(x))+1)(xcos⁡(x))xcos⁡(x)\left(\log{\left(x^{\cos{\left(x \right)}} \right)} + 1\right) \left(x^{\cos{\left(x \right)}}\right)^{x^{\cos{\left(x \right)}}}

Respuesta:

(log⁡(xcos⁡(x))+1)(xcos⁡(x))xcos⁡(x)\left(\log{\left(x^{\cos{\left(x \right)}} \right)} + 1\right) \left(x^{\cos{\left(x \right)}}\right)^{x^{\cos{\left(x \right)}}}

Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        / cos(x)\ / cos(x)                                                      \
        \x      / |x      *cos(x)    cos(x) /cos(x)                \            |
(sin(x))         *|-------------- + x      *|------ - log(x)*sin(x)|*log(sin(x))|
                  \    sin(x)               \  x                   /            /
(xcos⁡(x)(−log⁡(x)sin⁡(x)+cos⁡(x)x)log⁡(sin⁡(x))+xcos⁡(x)cos⁡(x)sin⁡(x))sin⁡xcos⁡(x)(x)\left(x^{\cos{\left(x \right)}} \left(- \log{\left(x \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{x^{\cos{\left(x \right)}} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{x^{\cos{\left(x \right)}}}{\left(x \right)}
Simplificar
Segunda derivada [src] 
                          /                                                                                                                                                                      /                cos(x)\       \
                / cos(x)\ |                                                            2                           2                  2                                                        2*|log(x)*sin(x) - ------|*cos(x)|
 cos(x)         \x      / |      cos(x) //                cos(x)\               cos(x)\    /                cos(x)\                cos (x)   /cos(x)                   2*sin(x)\                 \                  x   /       |
x      *(sin(x))         *|-1 + x      *||log(x)*sin(x) - ------|*log(sin(x)) - ------|  + |log(x)*sin(x) - ------| *log(sin(x)) - ------- - |------ + cos(x)*log(x) + --------|*log(sin(x)) - ---------------------------------|
                          |             \\                  x   /               sin(x)/    \                  x   /                   2      |   2                        x    |                             sin(x)             |
                          \                                                                                                        sin (x)   \  x                              /                                                /
xcos⁡(x)(xcos⁡(x)((log⁡(x)sin⁡(x)−cos⁡(x)x)log⁡(sin⁡(x))−cos⁡(x)sin⁡(x))2+(log⁡(x)sin⁡(x)−cos⁡(x)x)2log⁡(sin⁡(x))−2(log⁡(x)sin⁡(x)−cos⁡(x)x)cos⁡(x)sin⁡(x)−(log⁡(x)cos⁡(x)+2sin⁡(x)x+cos⁡(x)x2)log⁡(sin⁡(x))−1−cos⁡2(x)sin⁡2(x))sin⁡xcos⁡(x)(x)x^{\cos{\left(x \right)}} \left(x^{\cos{\left(x \right)}} \left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} + \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{2} \log{\left(\sin{\left(x \right)} \right)} - \frac{2 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \log{\left(\sin{\left(x \right)} \right)} - 1 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{x^{\cos{\left(x \right)}}}{\left(x \right)}
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Tercera derivada [src] 
                          /                                                                                                                                                                                                                          /cos(x)                   2*sin(x)\                                                                                                                                                                                                                                            2                                                                                                                         \
                          |                                                                                                                                                                                                                        3*|------ + cos(x)*log(x) + --------|*cos(x)                                                             /                                                                                                          /                cos(x)\       \     /                cos(x)\                2    /                cos(x)\                                                                             |
                / cos(x)\ |                                                                                                                        3                           3                               3                                     |   2                        x    |                                                                    |       2                                                                                2               2*|log(x)*sin(x) - ------|*cos(x)|   3*|log(x)*sin(x) - ------| *cos(x)   3*cos (x)*|log(x)*sin(x) - ------|                                                                             |
 cos(x)         \x      / |/                3*cos(x)   2*cos(x)   3*sin(x)\                2*cos(x) //                cos(x)\               cos(x)\    /                cos(x)\                3*cos(x)   2*cos (x)   2*cos(x)                       \  x                              /             cos(x) //                cos(x)\               cos(x)\ |    cos (x)   /cos(x)                   2*sin(x)\               /                cos(x)\                  \                  x   /       |     \                  x   /                     \                  x   /     /                cos(x)\ /cos(x)                   2*sin(x)\            |
x      *(sin(x))         *||log(x)*sin(x) - -------- + -------- + --------|*log(sin(x)) - x        *||log(x)*sin(x) - ------|*log(sin(x)) - ------|  - |log(x)*sin(x) - ------| *log(sin(x)) - -------- + --------- + -------- + 3*log(x)*sin(x) - -------------------------------------------- + 3*x      *||log(x)*sin(x) - ------|*log(sin(x)) - ------|*|1 + ------- + |------ + cos(x)*log(x) + --------|*log(sin(x)) - |log(x)*sin(x) - ------| *log(sin(x)) + ---------------------------------| + ---------------------------------- + ---------------------------------- + 3*|log(x)*sin(x) - ------|*|------ + cos(x)*log(x) + --------|*log(sin(x))|
                          ||                   x           3          2   |                         \\                  x   /               sin(x)/    \                  x   /                   x           3        sin(x)                                         sin(x)                                \\                  x   /               sin(x)/ |       2      |   2                        x    |               \                  x   /                              sin(x)             |                 sin(x)                                 2                      \                  x   / |   2                        x    |            |
                          \\                              x          x    /                                                                                                                                sin (x)                                                                                                                                          \    sin (x)   \  x                              /                                                                                        /                                                     sin (x)                                            \  x                              /            /
xcos⁡(x)(−x2cos⁡(x)((log⁡(x)sin⁡(x)−cos⁡(x)x)log⁡(sin⁡(x))−cos⁡(x)sin⁡(x))3+3xcos⁡(x)((log⁡(x)sin⁡(x)−cos⁡(x)x)log⁡(sin⁡(x))−cos⁡(x)sin⁡(x))(−(log⁡(x)sin⁡(x)−cos⁡(x)x)2log⁡(sin⁡(x))+2(log⁡(x)sin⁡(x)−cos⁡(x)x)cos⁡(x)sin⁡(x)+(log⁡(x)cos⁡(x)+2sin⁡(x)x+cos⁡(x)x2)log⁡(sin⁡(x))+1+cos⁡2(x)sin⁡2(x))−(log⁡(x)sin⁡(x)−cos⁡(x)x)3log⁡(sin⁡(x))+3(log⁡(x)sin⁡(x)−cos⁡(x)x)2cos⁡(x)sin⁡(x)+3(log⁡(x)sin⁡(x)−cos⁡(x)x)(log⁡(x)cos⁡(x)+2sin⁡(x)x+cos⁡(x)x2)log⁡(sin⁡(x))+3(log⁡(x)sin⁡(x)−cos⁡(x)x)cos⁡2(x)sin⁡2(x)−3(log⁡(x)cos⁡(x)+2sin⁡(x)x+cos⁡(x)x2)cos⁡(x)sin⁡(x)+(log⁡(x)sin⁡(x)−3cos⁡(x)x+3sin⁡(x)x2+2cos⁡(x)x3)log⁡(sin⁡(x))+3log⁡(x)sin⁡(x)+2cos⁡(x)sin⁡(x)+2cos⁡3(x)sin⁡3(x)−3cos⁡(x)x)sin⁡xcos⁡(x)(x)x^{\cos{\left(x \right)}} \left(- x^{2 \cos{\left(x \right)}} \left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} + 3 x^{\cos{\left(x \right)}} \left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \log{\left(\sin{\left(x \right)} \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(- \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{2} \log{\left(\sin{\left(x \right)} \right)} + \frac{2 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \log{\left(\sin{\left(x \right)} \right)} + 1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) - \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{3} \log{\left(\sin{\left(x \right)} \right)} + \frac{3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + 3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x} + \frac{3 \sin{\left(x \right)}}{x^{2}} + \frac{2 \cos{\left(x \right)}}{x^{3}}\right) \log{\left(\sin{\left(x \right)} \right)} + 3 \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{x}\right) \sin^{x^{\cos{\left(x \right)}}}{\left(x \right)}
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Gráfico
Derivada de y=(sinx)^x^cosx
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