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x*x^sen(x)
Derivada de la función/ sen(x)/ x*x^sen(x)

Derivada de x*x^sen(x)

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
xxsin⁡(x)x x^{\sin{\left(x \right)}} 
x*x^sin(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)=xf{\left(x \right)} = x; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Según el principio, aplicamos: xx tenemos 11

    g(x)=xsin⁡(x)g{\left(x \right)} = x^{\sin{\left(x \right)}}; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    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)}

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-100100
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Primera derivada [src] 
 sin(x)      sin(x) /sin(x)                \
x       + x*x      *|------ + cos(x)*log(x)|
                    \  x                   /
xxsin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)+xsin⁡(x)x x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) + x^{\sin{\left(x \right)}}
Simplificar
Segunda derivada [src] 
        /  /                        2                                    \                             \
 sin(x) |  |/sin(x)                \    sin(x)                   2*cos(x)|   2*sin(x)                  |
x      *|x*||------ + cos(x)*log(x)|  - ------ - log(x)*sin(x) + --------| + -------- + 2*cos(x)*log(x)|
        |  |\  x                   /       2                        x    |      x                      |
        \  \                              x                              /                             /
xsin⁡(x)(x((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)x^{\sin{\left(x \right)}} \left(x \left(\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                                                                                                                  \                                        \
 sin(x) |  /sin(x)                \      |  /sin(x)                \                    2*sin(x)   3*sin(x)   3*cos(x)     /sin(x)                \ /sin(x)                   2*cos(x)\|   3*sin(x)                     6*cos(x)|
x      *|3*|------ + cos(x)*log(x)|  - x*|- |------ + cos(x)*log(x)|  + cos(x)*log(x) - -------- + -------- + -------- + 3*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------|| - -------- - 3*log(x)*sin(x) + --------|
        |  \  x                   /      |  \  x                   /                        3         x           2        \  x                   / |   2                        x    ||       2                           x    |
        \                                \                                                 x                     x                                  \  x                              //      x                                 /
xsin⁡(x)(−x(−(log⁡(x)cos⁡(x)+sin⁡(x)x)3+3(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)+3(log⁡(x)cos⁡(x)+sin⁡(x)x)2−3log⁡(x)sin⁡(x)+6cos⁡(x)x−3sin⁡(x)x2)x^{\sin{\left(x \right)}} \left(- x \left(- \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} + 3 \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) + 3 \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*x^sen(x)
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