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y=(sinx)^sqrtx
Derivada de la función/ sqrtx/ (sinx)/ y=(sinx)^sqrtx

Derivada de y=(sinx)^sqrtx

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

Gráfico:

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Definida a trozos:

Solución

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

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

    Perola derivada

    xx2(log⁡(x)+1)x^{\frac{\sqrt{x}}{2}} \left(\log{\left(\sqrt{x} \right)} + 1\right)

  2. Simplificamos:

    xx2(log⁡(x)+2)2\frac{x^{\frac{\sqrt{x}}{2}} \left(\log{\left(x \right)} + 2\right)}{2}

Respuesta:

xx2(log⁡(x)+2)2\frac{x^{\frac{\sqrt{x}}{2}} \left(\log{\left(x \right)} + 2\right)}{2}

Gráfica
02468-8-6-4-2-10102.5-2.5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
          ___ /                ___       \
        \/ x  |log(sin(x))   \/ x *cos(x)|
(sin(x))     *|----------- + ------------|
              |      ___        sin(x)   |
              \  2*\/ x                  /
(xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\frac{\sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)}
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Segunda derivada [src] 
              /                                        2                                             \
              |          /                  ___       \                                              |
              |          |log(sin(x))   2*\/ x *cos(x)|                                              |
              |          |----------- + --------------|                                              |
          ___ |          |     ___          sin(x)    |                                   ___    2   |
        \/ x  |    ___   \   \/ x                     /    log(sin(x))      cos(x)      \/ x *cos (x)|
(sin(x))     *|- \/ x  + ------------------------------- - ----------- + ------------ - -------------|
              |                         4                        3/2       ___                2      |
              \                                               4*x        \/ x *sin(x)      sin (x)   /
(−x−xcos⁡2(x)sin⁡2(x)+(2xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))x)24+cos⁡(x)xsin⁡(x)−log⁡(sin⁡(x))4x32)sin⁡x(x)\left(- \sqrt{x} - \frac{\sqrt{x} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right)^{2}}{4} + \frac{\cos{\left(x \right)}}{\sqrt{x} \sin{\left(x \right)}} - \frac{\log{\left(\sin{\left(x \right)} \right)}}{4 x^{\frac{3}{2}}}\right) \sin^{\sqrt{x}}{\left(x \right)}
Simplificar
Tercera derivada [src] 
              /                                          3                                                                                                                                                                                 \
              |            /                  ___       \      /                  ___       \ /                                           ___    2   \                                                                                     |
              |            |log(sin(x))   2*\/ x *cos(x)|      |log(sin(x))   2*\/ x *cos(x)| |    ___   log(sin(x))     4*cos(x)     4*\/ x *cos (x)|                                                                                     |
              |            |----------- + --------------|    3*|----------- + --------------|*|4*\/ x  + ----------- - ------------ + ---------------|                                                                                     |
          ___ |            |     ___          sin(x)    |      |     ___          sin(x)    | |               3/2        ___                 2       |                       ___    3          ___                  2                      |
        \/ x  |     3      \   \/ x                     /      \   \/ x                     / \              x         \/ x *sin(x)       sin (x)    /   3*log(sin(x))   2*\/ x *cos (x)   2*\/ x *cos(x)      3*cos (x)         3*cos(x)  |
(sin(x))     *|- ------- + ------------------------------- - ----------------------------------------------------------------------------------------- + ------------- + --------------- + -------------- - --------------- - -------------|
              |      ___                  8                                                              8                                                      5/2             3              sin(x)           ___    2         3/2       |
              \  2*\/ x                                                                                                                                      8*x             sin (x)                        2*\/ x *sin (x)   4*x   *sin(x)/
(2xcos⁡(x)sin⁡(x)+2xcos⁡3(x)sin⁡3(x)+(2xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))x)38−3(2xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))x)(4x+4xcos⁡2(x)sin⁡2(x)−4cos⁡(x)xsin⁡(x)+log⁡(sin⁡(x))x32)8−32x−3cos⁡2(x)2xsin⁡2(x)−3cos⁡(x)4x32sin⁡(x)+3log⁡(sin⁡(x))8x52)sin⁡x(x)\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \sqrt{x} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right)^{3}}{8} - \frac{3 \left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right) \left(4 \sqrt{x} + \frac{4 \sqrt{x} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 \cos{\left(x \right)}}{\sqrt{x} \sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x^{\frac{3}{2}}}\right)}{8} - \frac{3}{2 \sqrt{x}} - \frac{3 \cos^{2}{\left(x \right)}}{2 \sqrt{x} \sin^{2}{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{4 x^{\frac{3}{2}} \sin{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)}}{8 x^{\frac{5}{2}}}\right) \sin^{\sqrt{x}}{\left(x \right)}
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Gráfico
Derivada de y=(sinx)^sqrtx
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