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x*sin(x)^tg(x)

Derivada de x*sin(x)^tg(x)

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

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Solución

Ha introducido [src]
     tan(x)   
x*sin      (x)
$$x \sin^{\tan{\left(x \right)}}{\left(x \right)}$$
x*sin(x)^tan(x)
Solución detallada
  1. Se aplica la regla de la derivada de una multiplicación:

    ; calculamos :

    1. Según el principio, aplicamos: tenemos

    ; calculamos :

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

      Perola derivada

    Como resultado de:


Respuesta:

Gráfica
Primera derivada [src]
   tan(x)           tan(x)    //       2   \               cos(x)*tan(x)\
sin      (x) + x*sin      (x)*|\1 + tan (x)/*log(sin(x)) + -------------|
                              \                                sin(x)   /
$$x \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\tan{\left(x \right)}}{\left(x \right)} + \sin^{\tan{\left(x \right)}}{\left(x \right)}$$
Segunda derivada [src]
             /  /                                           2               2               /       2   \                                            \                                                \
   tan(x)    |  |//       2   \               cos(x)*tan(x)\             cos (x)*tan(x)   2*\1 + tan (x)/*cos(x)     /       2   \                   |     /       2   \               2*cos(x)*tan(x)|
sin      (x)*|x*||\1 + tan (x)/*log(sin(x)) + -------------|  - tan(x) - -------------- + ---------------------- + 2*\1 + tan (x)/*log(sin(x))*tan(x)| + 2*\1 + tan (x)/*log(sin(x)) + ---------------|
             |  |\                                sin(x)   /                   2                  sin(x)                                             |                                      sin(x)    |
             \  \                                                           sin (x)                                                                  /                                                /
$$\left(x \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - \tan{\left(x \right)} - \frac{\cos^{2}{\left(x \right)} \tan{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{2 \cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\tan{\left(x \right)}}{\left(x \right)}$$
Tercera derivada [src]
             /                                                         2     /                                                3                              2                                                             /             2               /       2   \                                            \        2    /       2   \        3                                                                       /       2   \              \        2               /       2   \                                            \
   tan(x)    |              //       2   \               cos(x)*tan(x)\      |     //       2   \               cos(x)*tan(x)\         2        /       2   \                  //       2   \               cos(x)*tan(x)\ |          cos (x)*tan(x)   2*\1 + tan (x)/*cos(x)     /       2   \                   |   3*cos (x)*\1 + tan (x)/   2*cos (x)*tan(x)   2*cos(x)*tan(x)        2    /       2   \               6*\1 + tan (x)/*cos(x)*tan(x)|   3*cos (x)*tan(x)   6*\1 + tan (x)/*cos(x)     /       2   \                   |
sin      (x)*|-3*tan(x) + 3*|\1 + tan (x)/*log(sin(x)) + -------------|  + x*|-3 + |\1 + tan (x)/*log(sin(x)) + -------------|  - 3*tan (x) + 2*\1 + tan (x)/ *log(sin(x)) + 3*|\1 + tan (x)/*log(sin(x)) + -------------|*|-tan(x) - -------------- + ---------------------- + 2*\1 + tan (x)/*log(sin(x))*tan(x)| - ----------------------- + ---------------- + --------------- + 4*tan (x)*\1 + tan (x)/*log(sin(x)) + -----------------------------| - ---------------- + ---------------------- + 6*\1 + tan (x)/*log(sin(x))*tan(x)|
             |              \                                sin(x)   /      |     \                                sin(x)   /                                                 \                                sin(x)   / |                2                  sin(x)                                             |              2                     3                sin(x)                                                         sin(x)           |          2                   sin(x)                                             |
             \                                                               \                                                                                                                                             \             sin (x)                                                                  /           sin (x)               sin (x)                                                                                             /       sin (x)                                                                   /
$$\left(x \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - \tan{\left(x \right)} - \frac{\cos^{2}{\left(x \right)} \tan{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\sin{\left(x \right)} \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - 3 \tan^{2}{\left(x \right)} - 3 + \frac{2 \cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)} \tan{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} + 6 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - 3 \tan{\left(x \right)} - \frac{3 \cos^{2}{\left(x \right)} \tan{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{\tan{\left(x \right)}}{\left(x \right)}$$
Gráfico
Derivada de x*sin(x)^tg(x)