Derivada de (xsinx)^(8ln(x-sinx))

Solución

Ha introducido [src]

          8*log(x - sin(x))
(x*sin(x))

$$\left(x \sin{\left(x \right)}\right)^{8 \log{\left(x - \sin{\left(x \right)} \right)}}$$

(x*sin(x))^(8*log(x - sin(x)))

Solución detallada

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

Perola derivada

$\left(8 \log{\left(x - \sin{\left(x \right)} \right)}\right)^{8 \log{\left(x - \sin{\left(x \right)} \right)}} \left(\log{\left(8 \log{\left(x - \sin{\left(x \right)} \right)} \right)} + 1\right)$

Respuesta:

$\left(8 \log{\left(x - \sin{\left(x \right)} \right)}\right)^{8 \log{\left(x - \sin{\left(x \right)} \right)}} \left(\log{\left(8 \log{\left(x - \sin{\left(x \right)} \right)} \right)} + 1\right)$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

          8*log(x - sin(x)) /8*(1 - cos(x))*log(x*sin(x))   8*(x*cos(x) + sin(x))*log(x - sin(x))\
(x*sin(x))                 *|---------------------------- + -------------------------------------|
                            \         x - sin(x)                           x*sin(x)              /

$$\left(x \sin{\left(x \right)}\right)^{8 \log{\left(x - \sin{\left(x \right)} \right)}} \left(\frac{8 \left(1 - \cos{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)}}{x - \sin{\left(x \right)}} + \frac{8 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}}\right)$$

Simplificar

Segunda derivada [src]

                              /                                                                     2                                       2                                                                                                                                                                                \
            8*log(x - sin(x)) |  /(-1 + cos(x))*log(x*sin(x))   (x*cos(x) + sin(x))*log(x - sin(x))\    log(x*sin(x))*sin(x)   (-1 + cos(x)) *log(x*sin(x))   (-2*cos(x) + x*sin(x))*log(x - sin(x))   (x*cos(x) + sin(x))*log(x - sin(x))   (x*cos(x) + sin(x))*cos(x)*log(x - sin(x))   2*(-1 + cos(x))*(x*cos(x) + sin(x))|
8*(x*sin(x))                 *|8*|--------------------------- - -----------------------------------|  + -------------------- - ---------------------------- - -------------------------------------- - ----------------------------------- - ------------------------------------------ - -----------------------------------|
                              |  \         x - sin(x)                         x*sin(x)             /         x - sin(x)                           2                          x*sin(x)                                2                                            2                              x*(x - sin(x))*sin(x)       |
                              \                                                                                                       (x - sin(x))                                                                  x *sin(x)                                x*sin (x)                                                       /

$$8 \left(x \sin{\left(x \right)}\right)^{8 \log{\left(x - \sin{\left(x \right)} \right)}} \left(8 \left(\frac{\left(\cos{\left(x \right)} - 1\right) \log{\left(x \sin{\left(x \right)} \right)}}{x - \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}}\right)^{2} + \frac{\log{\left(x \sin{\left(x \right)} \right)} \sin{\left(x \right)}}{x - \sin{\left(x \right)}} - \frac{\left(\cos{\left(x \right)} - 1\right)^{2} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x - \sin{\left(x \right)}\right)^{2}} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right)}{x \left(x - \sin{\left(x \right)}\right) \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x^{2} \sin{\left(x \right)}}\right)$$

Simplificar

Tercera derivada [src]

                              /                                                                        3                                                                          /             2                                                                                                                                                                                                       \                                         3                                                                                                                                                                                                                                                                2                            2                                                                                                                                                                                                                                                                    \
            8*log(x - sin(x)) |     /(-1 + cos(x))*log(x*sin(x))   (x*cos(x) + sin(x))*log(x - sin(x))\       /(-1 + cos(x))*log(x*sin(x))   (x*cos(x) + sin(x))*log(x - sin(x))\ |(-1 + cos(x)) *log(x*sin(x))   log(x*sin(x))*sin(x)   (-2*cos(x) + x*sin(x))*log(x - sin(x))   (x*cos(x) + sin(x))*log(x - sin(x))   (x*cos(x) + sin(x))*cos(x)*log(x - sin(x))   2*(-1 + cos(x))*(x*cos(x) + sin(x))|   cos(x)*log(x*sin(x))   2*(-1 + cos(x)) *log(x*sin(x))   3*(x*cos(x) + sin(x))   (x*cos(x) + sin(x))*log(x - sin(x))   (3*sin(x) + x*cos(x))*log(x - sin(x))   2*(x*cos(x) + sin(x))*log(x - sin(x))   2*(-2*cos(x) + x*sin(x))*log(x - sin(x))   3*(-1 + cos(x))*log(x*sin(x))*sin(x)   3*(-1 + cos(x)) *(x*cos(x) + sin(x))   2*cos (x)*(x*cos(x) + sin(x))*log(x - sin(x))   2*(-2*cos(x) + x*sin(x))*cos(x)*log(x - sin(x))   2*(x*cos(x) + sin(x))*cos(x)*log(x - sin(x))   3*(-1 + cos(x))*(-2*cos(x) + x*sin(x))   3*(-1 + cos(x))*(x*cos(x) + sin(x))   3*(-1 + cos(x))*(x*cos(x) + sin(x))*cos(x)|
8*(x*sin(x))                 *|- 64*|--------------------------- - -----------------------------------|  + 24*|--------------------------- - -----------------------------------|*|---------------------------- - -------------------- + -------------------------------------- + ----------------------------------- + ------------------------------------------ + -----------------------------------| + -------------------- - ------------------------------ + --------------------- + ----------------------------------- - ------------------------------------- + ------------------------------------- + ---------------------------------------- + ------------------------------------ - ------------------------------------ + --------------------------------------------- + ----------------------------------------------- + -------------------------------------------- + -------------------------------------- + ----------------------------------- + ------------------------------------------|
                              |     \         x - sin(x)                         x*sin(x)             /       \         x - sin(x)                         x*sin(x)             / |                   2                x - sin(x)                       x*sin(x)                                2                                            2                              x*(x - sin(x))*sin(x)       |        x - sin(x)                            3                x*(x - sin(x))                    x*sin(x)                               x*sin(x)                                3                                        2                                                 2                                    2                                        3                                                2                                           2    2                               x*(x - sin(x))*sin(x)                    2                                                         2             |
                              \                                                                                                                                                   \       (x - sin(x))                                                                                         x *sin(x)                                x*sin (x)                                                       /                                  (x - sin(x))                                                                                                                                 x *sin(x)                                x *sin(x)                              (x - sin(x))                       x*(x - sin(x)) *sin(x)                            x*sin (x)                                        x*sin (x)                                       x *sin (x)                                                                    x *(x - sin(x))*sin(x)                   x*(x - sin(x))*sin (x)          /

$$8 \left(x \sin{\left(x \right)}\right)^{8 \log{\left(x - \sin{\left(x \right)} \right)}} \left(- 64 \left(\frac{\left(\cos{\left(x \right)} - 1\right) \log{\left(x \sin{\left(x \right)} \right)}}{x - \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}}\right)^{3} + 24 \left(\frac{\left(\cos{\left(x \right)} - 1\right) \log{\left(x \sin{\left(x \right)} \right)}}{x - \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}}\right) \left(- \frac{\log{\left(x \sin{\left(x \right)} \right)} \sin{\left(x \right)}}{x - \sin{\left(x \right)}} + \frac{\left(\cos{\left(x \right)} - 1\right)^{2} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x - \sin{\left(x \right)}\right)^{2}} + \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \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(\cos{\left(x \right)} - 1\right)}{x \left(x - \sin{\left(x \right)}\right) \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x^{2} \sin{\left(x \right)}}\right) + \frac{\log{\left(x \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x - \sin{\left(x \right)}} + \frac{3 \left(\cos{\left(x \right)} - 1\right) \log{\left(x \sin{\left(x \right)} \right)} \sin{\left(x \right)}}{\left(x - \sin{\left(x \right)}\right)^{2}} - \frac{2 \left(\cos{\left(x \right)} - 1\right)^{3} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x - \sin{\left(x \right)}\right)^{3}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)}}{x \sin^{3}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x \sin{\left(x \right)}} + \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right)}{x \left(x - \sin{\left(x \right)}\right) \sin{\left(x \right)}} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right) \cos{\left(x \right)}}{x \left(x - \sin{\left(x \right)}\right) \sin^{2}{\left(x \right)}} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \left(x - \sin{\left(x \right)}\right)} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right)^{2}}{x \left(x - \sin{\left(x \right)}\right)^{2} \sin{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{x^{2} \sin^{2}{\left(x \right)}} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\cos{\left(x \right)} - 1\right)}{x^{2} \left(x - \sin{\left(x \right)}\right) \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x - \sin{\left(x \right)} \right)}}{x^{3} \sin{\left(x \right)}}\right)$$

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Derivada de (xsinx)^(8ln(x-sinx))

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