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

Derivada de y=(sqrt(sinx))^x

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

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-200000200000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        x                             
        -                             
        2 /x*cos(x)      /  ________\\
(sin(x)) *|-------- + log\\/ sin(x) /|
          \2*sin(x)                  /
(xcos⁡(x)2sin⁡(x)+log⁡(sin⁡(x)))sin⁡x2(x)\left(\frac{x \cos{\left(x \right)}}{2 \sin{\left(x \right)}} + \log{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \sin^{\frac{x}{2}}{\left(x \right)}
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Segunda derivada [src] 
        x /               /     /  ________\   x*cos(x)\ /x*cos(x)              \            \
        - |               |2*log\\/ sin(x) / + --------|*|-------- + log(sin(x))|        2   |
        2 |  x   cos(x)   \                     sin(x) / \ sin(x)               /   x*cos (x)|
(sin(x)) *|- - + ------ + ------------------------------------------------------- - ---------|
          |  2   sin(x)                              4                                   2   |
          \                                                                         2*sin (x)/
(−x2−xcos⁡2(x)2sin⁡2(x)+(xcos⁡(x)sin⁡(x)+2log⁡(sin⁡(x)))(xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x)))4+cos⁡(x)sin⁡(x))sin⁡x2(x)\left(- \frac{x}{2} - \frac{x \cos^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)}} + \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)}{4} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\frac{x}{2}}{\left(x \right)}
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Tercera derivada [src] 
          /                                           /                    2   \                                  /                    2   \                                                                                  \
          |                  /x*cos(x)              \ |    2*cos(x)   x*cos (x)|   /     /  ________\   x*cos(x)\ |    2*cos(x)   x*cos (x)|                           2                                                      |
        x |                  |-------- + log(sin(x))|*|x - -------- + ---------|   |2*log\\/ sin(x) / + --------|*|x - -------- + ---------|   /x*cos(x)              \  /     /  ________\   x*cos(x)\                       |
        - |           2      \ sin(x)               / |     sin(x)        2    |   \                     sin(x) / |     sin(x)        2    |   |-------- + log(sin(x))| *|2*log\\/ sin(x) / + --------|        3              |
        2 |  3   3*cos (x)                            \                sin (x) /                                  \                sin (x) /   \ sin(x)               /  \                     sin(x) /   x*cos (x)   x*cos(x)|
(sin(x)) *|- - - --------- - --------------------------------------------------- - --------------------------------------------------------- + -------------------------------------------------------- + --------- + --------|
          |  2        2                               2                                                        4                                                          8                                   3        sin(x) |
          \      2*sin (x)                                                                                                                                                                                 sin (x)            /
(xcos⁡(x)sin⁡(x)+xcos⁡3(x)sin⁡3(x)+(xcos⁡(x)sin⁡(x)+2log⁡(sin⁡(x)))(xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x)))28−(xcos⁡(x)sin⁡(x)+2log⁡(sin⁡(x)))(x+xcos⁡2(x)sin⁡2(x)−2cos⁡(x)sin⁡(x))4−(xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x)))(x+xcos⁡2(x)sin⁡2(x)−2cos⁡(x)sin⁡(x))2−32−3cos⁡2(x)2sin⁡2(x))sin⁡x2(x)\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{x \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right)^{2}}{8} - \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \left(x + \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)}{4} - \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)}\right) \left(x + \frac{x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)}{2} - \frac{3}{2} - \frac{3 \cos^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)}}\right) \sin^{\frac{x}{2}}{\left(x \right)}
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Gráfico
Derivada de y=(sqrt(sinx))^x
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