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

Derivada de x^sinsinx

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

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

    Perola derivada

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

Respuesta:

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

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