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Derivada de (x*sin(x))^(i*n*x*sin(x))

Función f() - derivada -er orden en el punto
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Solución

Ha introducido [src]
          I*n*x*sin(x)
(x*sin(x))            
$$\left(x \sin{\left(x \right)}\right)^{x i n \sin{\left(x \right)}}$$
(x*sin(x))^(((i*n)*x)*sin(x))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Primera derivada [src]
          I*n*x*sin(x)                                                                      
(x*sin(x))            *((I*n*sin(x) + I*n*x*cos(x))*log(x*sin(x)) + I*n*(x*cos(x) + sin(x)))
$$\left(x \sin{\left(x \right)}\right)^{x i n \sin{\left(x \right)}} \left(i n \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) + \left(i n x \cos{\left(x \right)} + i n \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)}\right)$$
Segunda derivada [src]
                          /  /                                                                                 2\                                              \
             I*n*x*sin(x) |  |                                                              (x*cos(x) + sin(x)) |                        2                    2|
-n*(x*sin(x))            *|I*|-2*cos(x) + x*sin(x) + (-2*cos(x) + x*sin(x))*log(x*sin(x)) - --------------------| + n*(1 + log(x*sin(x))) *(x*cos(x) + sin(x)) |
                          \  \                                                                    x*sin(x)      /                                              /
$$- n \left(x \sin{\left(x \right)}\right)^{i n x \sin{\left(x \right)}} \left(n \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \left(\log{\left(x \sin{\left(x \right)} \right)} + 1\right)^{2} + i \left(x \sin{\left(x \right)} + \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} - 2 \cos{\left(x \right)} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2}}{x \sin{\left(x \right)}}\right)\right)$$
Tercera derivada [src]
                         /    /                                                                               2                      2                                                      \                                                                                                /                                                                                 2\\
            I*n*x*sin(x) |    |                                                            (x*cos(x) + sin(x))    (x*cos(x) + sin(x)) *cos(x)   3*(-2*cos(x) + x*sin(x))*(x*cos(x) + sin(x))|      2                    3                    3                                               |                                                              (x*cos(x) + sin(x)) ||
n*(x*sin(x))            *|- I*|3*sin(x) + x*cos(x) + (3*sin(x) + x*cos(x))*log(x*sin(x)) + -------------------- + --------------------------- + --------------------------------------------| - I*n *(1 + log(x*sin(x))) *(x*cos(x) + sin(x))  + 3*n*(1 + log(x*sin(x)))*(x*cos(x) + sin(x))*|-2*cos(x) + x*sin(x) + (-2*cos(x) + x*sin(x))*log(x*sin(x)) - --------------------||
                         |    |                                                                  2                              2                                 x*sin(x)                  |                                                                                                \                                                                    x*sin(x)      /|
                         \    \                                                                 x *sin(x)                  x*sin (x)                                                        /                                                                                                                                                                                    /
$$n \left(x \sin{\left(x \right)}\right)^{i n x \sin{\left(x \right)}} \left(- i n^{2} \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{3} \left(\log{\left(x \sin{\left(x \right)} \right)} + 1\right)^{3} + 3 n \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(\log{\left(x \sin{\left(x \right)} \right)} + 1\right) \left(x \sin{\left(x \right)} + \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} - 2 \cos{\left(x \right)} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2}}{x \sin{\left(x \right)}}\right) - i \left(x \cos{\left(x \right)} + \left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x \sin{\left(x \right)} \right)} + 3 \sin{\left(x \right)} + \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)^{2}}{x^{2} \sin{\left(x \right)}}\right)\right)$$