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(√x)^sinx
Derivada de la función/ (√x)^sinx

Derivada de (√x)^sinx

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

Gráfico:

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Definida a trozos:

Solución

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 sin(x)                             
 ------                             
   2    /          /  ___\   sin(x)\
x      *|cos(x)*log\\/ x / + ------|
        \                     2*x  /
xsin⁡(x)2(log⁡(x)cos⁡(x)+sin⁡(x)2x)x^{\frac{\sin{\left(x \right)}}{2}} \left(\log{\left(\sqrt{x} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{2 x}\right)
Simplificar
Segunda derivada [src] 
 sin(x) /                                      /sin(x)                \ /sin(x)               /  ___\\\
 ------ |                                      |------ + cos(x)*log(x)|*|------ + 2*cos(x)*log\\/ x /||
   2    |cos(x)      /  ___\          sin(x)   \  x                   / \  x                         /|
x      *|------ - log\\/ x /*sin(x) - ------ + -------------------------------------------------------|
        |  x                              2                               4                           |
        \                              2*x                                                            /
xsin⁡(x)2((2log⁡(x)cos⁡(x)+sin⁡(x)x)(log⁡(x)cos⁡(x)+sin⁡(x)x)4−log⁡(x)sin⁡(x)+cos⁡(x)x−sin⁡(x)2x2)x^{\frac{\sin{\left(x \right)}}{2}} \left(\frac{\left(2 \log{\left(\sqrt{x} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{4} - \log{\left(\sqrt{x} \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{2 x^{2}}\right)
Simplificar
Tercera derivada [src] 
        /                                                   /sin(x)                \ /sin(x)   2*cos(x)        /  ___\       \   /sin(x)               /  ___\\ /sin(x)                   2*cos(x)\                           2                               \
 sin(x) |                                                   |------ + cos(x)*log(x)|*|------ - -------- + 2*log\\/ x /*sin(x)|   |------ + 2*cos(x)*log\\/ x /|*|------ + log(x)*sin(x) - --------|   /sin(x)                \  /sin(x)               /  ___\\|
 ------ |                                                   \  x                   / |   2        x                          |   \  x                         / |   2                        x    |   |------ + cos(x)*log(x)| *|------ + 2*cos(x)*log\\/ x /||
   2    |sin(x)             /  ___\   3*sin(x)   3*cos(x)                            \  x                                    /                                  \  x                              /   \  x                   /  \  x                         /|
x      *|------ - cos(x)*log\\/ x / - -------- - -------- - ------------------------------------------------------------------ - ------------------------------------------------------------------ + --------------------------------------------------------|
        |   3                           2*x           2                                     2                                                                    4                                                               8                            |
        \  x                                       2*x                                                                                                                                                                                                        /
xsin⁡(x)2((2log⁡(x)cos⁡(x)+sin⁡(x)x)(log⁡(x)cos⁡(x)+sin⁡(x)x)28−(2log⁡(x)cos⁡(x)+sin⁡(x)x)(log⁡(x)sin⁡(x)−2cos⁡(x)x+sin⁡(x)x2)4−(log⁡(x)cos⁡(x)+sin⁡(x)x)(2log⁡(x)sin⁡(x)−2cos⁡(x)x+sin⁡(x)x2)2−log⁡(x)cos⁡(x)−3sin⁡(x)2x−3cos⁡(x)2x2+sin⁡(x)x3)x^{\frac{\sin{\left(x \right)}}{2}} \left(\frac{\left(2 \log{\left(\sqrt{x} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2}}{8} - \frac{\left(2 \log{\left(\sqrt{x} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right)}{4} - \frac{\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(2 \log{\left(\sqrt{x} \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right)}{2} - \log{\left(\sqrt{x} \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{2 x} - \frac{3 \cos{\left(x \right)}}{2 x^{2}} + \frac{\sin{\left(x \right)}}{x^{3}}\right)
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Gráfico
Derivada de (√x)^sinx
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