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Derivada de:
Derivada de x^-7
Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
Derivada de (x+7)^5
Derivada de 1/x^9
Expresiones idénticas
(x*sin(x))^(lnx*sin(x))
(x multiplicar por seno de (x)) en el grado (lnx multiplicar por seno de (x))
(x*sin(x))(lnx*sin(x))
x*sinxlnx*sinx
(xsin(x))^(lnxsin(x))
(xsin(x))(lnxsin(x))
xsinxlnxsinx
xsinx^lnxsinx
Expresiones semejantes
(x*sinx)^(lnx*sinx)
Expresiones con funciones
Seno sin
sin(x)*9^-x
sin(x)^(6)
sin(x)^(5*x)
sin(x)^4
sin(x/3+3)+2*x
Seno sin
sin(x)*9^-x
sin(x)^(6)
sin(x)^(5*x)
sin(x)^4
sin(x/3+3)+2*x

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

Derivada de (xsin(x))^(lnxsin(x))

Solución

Ha introducido [src]

          log(x)*sin(x)
(x*sin(x))

\left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)} \sin{\left(x \right)}}

(x*sin(x))^(log(x)*sin(x))

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

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Gráfico

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Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de (xsin(x))^(lnxsin(x))

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

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

Gráfico:

Definida a trozos:

Solución

Derivada de (xsin(x))^(lnxsin(x))