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x^(sin(x)*(-2))*x
Derivada de la función/ sin(x)/ x^(sin(x)*(-2))*x

Derivada de x^(sin(x)*(-2))*x

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

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Solución

Ha introducido [src] 
 sin(x)*(-2)  
x           *x
xx(−2)sin⁡(x)x x^{\left(-2\right) \sin{\left(x \right)}} 
x^(sin(x)*(-2))*x
Solución detallada

  1. Se aplica la regla de la derivada de una multiplicación:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

    f(x)=x(−2)sin⁡(x)f{\left(x \right)} = x^{\left(-2\right) \sin{\left(x \right)}}; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

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

      Perola derivada

      ((−2)sin⁡(x))(−2)sin⁡(x)(log⁡((−2)sin⁡(x))+1)\left(\left(-2\right) \sin{\left(x \right)}\right)^{\left(-2\right) \sin{\left(x \right)}} \left(\log{\left(\left(-2\right) \sin{\left(x \right)} \right)} + 1\right)

    g(x)=xg{\left(x \right)} = x; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Según el principio, aplicamos: xx tenemos 11

    Como resultado de: x((−2)sin⁡(x))(−2)sin⁡(x)(log⁡((−2)sin⁡(x))+1)+x(−2)sin⁡(x)x \left(\left(-2\right) \sin{\left(x \right)}\right)^{\left(-2\right) \sin{\left(x \right)}} \left(\log{\left(\left(-2\right) \sin{\left(x \right)} \right)} + 1\right) + x^{\left(-2\right) \sin{\left(x \right)}}

  2. Simplificamos:

    x(−2sin⁡(x))−2sin⁡(x)log⁡(−2sin⁡(x))+x(−2sin⁡(x))−2sin⁡(x)+x−2sin⁡(x)x \left(- 2 \sin{\left(x \right)}\right)^{- 2 \sin{\left(x \right)}} \log{\left(- 2 \sin{\left(x \right)} \right)} + x \left(- 2 \sin{\left(x \right)}\right)^{- 2 \sin{\left(x \right)}} + x^{- 2 \sin{\left(x \right)}}

Respuesta:

x(−2sin⁡(x))−2sin⁡(x)log⁡(−2sin⁡(x))+x(−2sin⁡(x))−2sin⁡(x)+x−2sin⁡(x)x \left(- 2 \sin{\left(x \right)}\right)^{- 2 \sin{\left(x \right)}} \log{\left(- 2 \sin{\left(x \right)} \right)} + x \left(- 2 \sin{\left(x \right)}\right)^{- 2 \sin{\left(x \right)}} + x^{- 2 \sin{\left(x \right)}}

Gráfica
02468-8-6-4-2-1010-5001000
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Primera derivada [src] 
 sin(x)*(-2)      sin(x)*(-2) /  2*sin(x)                  \
x            + x*x           *|- -------- - 2*cos(x)*log(x)|
                              \     x                      /
xx(−2)sin⁡(x)(−2log⁡(x)cos⁡(x)−2sin⁡(x)x)+x(−2)sin⁡(x)x x^{\left(-2\right) \sin{\left(x \right)}} \left(- 2 \log{\left(x \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x}\right) + x^{\left(-2\right) \sin{\left(x \right)}}
Simplificar
Segunda derivada [src] 
             /  /                          2                                    \                             \
   -2*sin(x) |  |  /sin(x)                \    sin(x)                   2*cos(x)|   2*sin(x)                  |
2*x         *|x*|2*|------ + cos(x)*log(x)|  + ------ + log(x)*sin(x) - --------| - -------- - 2*cos(x)*log(x)|
             |  |  \  x                   /       2                        x    |      x                      |
             \  \                                x                              /                             /
2x−2sin⁡(x)(x(2(log⁡(x)cos⁡(x)+sin⁡(x)x)2+log⁡(x)sin⁡(x)−2cos⁡(x)x+sin⁡(x)x2)−2log⁡(x)cos⁡(x)−2sin⁡(x)x)2 x^{- 2 \sin{\left(x \right)}} \left(x \left(2 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} + \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) - 2 \log{\left(x \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x}\right)
Simplificar
Tercera derivada [src] 
             /                          2     /                          3                                                                                                                  \                                        \
   -2*sin(x) |  /sin(x)                \      |  /sin(x)                \                    3*sin(x)   3*cos(x)   2*sin(x)     /sin(x)                \ /sin(x)                   2*cos(x)\|   6*cos(x)   3*sin(x)                  |
2*x         *|6*|------ + cos(x)*log(x)|  - x*|4*|------ + cos(x)*log(x)|  - cos(x)*log(x) - -------- - -------- + -------- + 6*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------|| - -------- + -------- + 3*log(x)*sin(x)|
             |  \  x                   /      |  \  x                   /                       x           2          3        \  x                   / |   2                        x    ||      x           2                     |
             \                                \                                                            x          x                                  \  x                              //                 x                      /
2x−2sin⁡(x)(−x(4(log⁡(x)cos⁡(x)+sin⁡(x)x)3+6(log⁡(x)cos⁡(x)+sin⁡(x)x)(log⁡(x)sin⁡(x)−2cos⁡(x)x+sin⁡(x)x2)−log⁡(x)cos⁡(x)−3sin⁡(x)x−3cos⁡(x)x2+2sin⁡(x)x3)+6(log⁡(x)cos⁡(x)+sin⁡(x)x)2+3log⁡(x)sin⁡(x)−6cos⁡(x)x+3sin⁡(x)x2)2 x^{- 2 \sin{\left(x \right)}} \left(- x \left(4 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} + 6 \left(\log{\left(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) - \log{\left(x \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x} - \frac{3 \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3}}\right) + 6 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} + 3 \log{\left(x \right)} \sin{\left(x \right)} - \frac{6 \cos{\left(x \right)}}{x} + \frac{3 \sin{\left(x \right)}}{x^{2}}\right)
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Gráfico
Derivada de x^(sin(x)*(-2))*x
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