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Expresiones idénticas
x^(sin(x)*cos(x))
x en el grado ( seno de (x) multiplicar por coseno de (x))
x(sin(x)*cos(x))
xsinx*cosx
x^(sin(x)cos(x))
x(sin(x)cos(x))
xsinxcosx
x^sinxcosx
Expresiones semejantes
x^(sinx*cosx)

Derivada de la función/ cos(x)/ sin(x)/ x^(sin(x)*cos(x))

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

Solución

Ha introducido [src]

 sin(x)*cos(x)
x

$$x^{\sin{\left(x \right)} \cos{\left(x \right)}}$$

x^(sin(x)*cos(x))

Solución detallada

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

Perola derivada

$\left(\sin{\left(x \right)} \cos{\left(x \right)}\right)^{\sin{\left(x \right)} \cos{\left(x \right)}} \left(\log{\left(\sin{\left(x \right)} \cos{\left(x \right)} \right)} + 1\right)$
Simplificamos:

$\left(\frac{\sin{\left(2 x \right)}}{2}\right)^{\frac{\sin{\left(2 x \right)}}{2}} \left(\log{\left(\frac{\sin{\left(2 x \right)}}{2} \right)} + 1\right)$

Respuesta:

$\left(\frac{\sin{\left(2 x \right)}}{2}\right)^{\frac{\sin{\left(2 x \right)}}{2}} \left(\log{\left(\frac{\sin{\left(2 x \right)}}{2} \right)} + 1\right)$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

 sin(x)*cos(x) //   2         2   \          cos(x)*sin(x)\
x             *|\cos (x) - sin (x)/*log(x) + -------------|
               \                                   x      /

$$x^{\sin{\left(x \right)} \cos{\left(x \right)}} \left(\left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \log{\left(x \right)} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{x}\right)$$

Simplificar

Segunda derivada [src]

               /                                            2      2         2         2         2                                            \
 cos(x)*sin(x) |//   2         2   \          cos(x)*sin(x)\    cos (x)   sin (x)   sin (x) - cos (x)   cos(x)*sin(x)                         |
x             *||\sin (x) - cos (x)/*log(x) - -------------|  + ------- - ------- - ----------------- - ------------- - 4*cos(x)*log(x)*sin(x)|
               |\                                   x      /       x         x              x                  2                              |
               \                                                                                              x                               /

$$x^{\sin{\left(x \right)} \cos{\left(x \right)}} \left(\left(\left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \log{\left(x \right)} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{x}\right)^{2} - 4 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)} - \frac{\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}}{x} - \frac{\sin^{2}{\left(x \right)}}{x} + \frac{\cos^{2}{\left(x \right)}}{x} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{x^{2}}\right)$$

Simplificar

Tercera derivada [src]

               /                                              3      2         2                              2           2                                                     /   2         2         2         2                                            \                                                        \
 cos(x)*sin(x) |  //   2         2   \          cos(x)*sin(x)\    sin (x) - cos (x)        2             2*cos (x)   2*sin (x)     //   2         2   \          cos(x)*sin(x)\ |sin (x)   sin (x) - cos (x)   cos (x)   cos(x)*sin(x)                         |        2             12*cos(x)*sin(x)   2*cos(x)*sin(x)|
x             *|- |\sin (x) - cos (x)/*log(x) - -------------|  + ----------------- - 4*cos (x)*log(x) - --------- + --------- + 3*|\sin (x) - cos (x)/*log(x) - -------------|*|------- + ----------------- - ------- + ------------- + 4*cos(x)*log(x)*sin(x)| + 4*sin (x)*log(x) - ---------------- + ---------------|
               |  \                                   x      /             2                                  2           2        \                                   x      / |   x              x              x             2                              |                             x                   3      |
               \                                                          x                                  x           x                                                      \                                              x                               /                                                x       /

$$x^{\sin{\left(x \right)} \cos{\left(x \right)}} \left(- \left(\left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \log{\left(x \right)} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{x}\right)^{3} + 3 \left(\left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \log{\left(x \right)} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{x}\right) \left(4 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x} - \frac{\cos^{2}{\left(x \right)}}{x} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{x^{2}}\right) + 4 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 4 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{12 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}}{x^{2}} + \frac{2 \sin^{2}{\left(x \right)}}{x^{2}} - \frac{2 \cos^{2}{\left(x \right)}}{x^{2}} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{x^{3}}\right)$$

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Gráfico

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Expresiones idénticas

Expresiones semejantes

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

Gráfico:

Definida a trozos:

Solución