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(x*sin(x))^(ln(x*x+1))

Derivada de (x*sin(x))^(ln(x*x+1))

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

Gráfico:

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Solución

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

    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
          log(x*x + 1) /2*x*log(x*sin(x))   (x*cos(x) + sin(x))*log(x*x + 1)\
(x*sin(x))            *|----------------- + --------------------------------|
                       \     x*x + 1                    x*sin(x)            /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x x + 1 \right)}} \left(\frac{2 x \log{\left(x \sin{\left(x \right)} \right)}}{x x + 1} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x x + 1 \right)}}{x \sin{\left(x \right)}}\right)$$
Segunda derivada [src]
                      /                                                     2                                                                                                                                                                               \
             /     2\ |/                                           /     2\\                         2                                                                   /     2\                          /     2\                                 /     2\|
          log\1 + x / ||2*x*log(x*sin(x))   (x*cos(x) + sin(x))*log\1 + x /|    2*log(x*sin(x))   4*x *log(x*sin(x))   4*(x*cos(x) + sin(x))   (-2*cos(x) + x*sin(x))*log\1 + x /   (x*cos(x) + sin(x))*log\1 + x /   (x*cos(x) + sin(x))*cos(x)*log\1 + x /|
(x*sin(x))           *||----------------- + -------------------------------|  + --------------- - ------------------ + --------------------- - ---------------------------------- - ------------------------------- - --------------------------------------|
                      ||           2                    x*sin(x)           |              2                   2           /     2\                          x*sin(x)                            2                                        2                  |
                      |\      1 + x                                        /         1 + x            /     2\            \1 + x /*sin(x)                                                      x *sin(x)                            x*sin (x)               |
                      \                                                                               \1 + x /                                                                                                                                              /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x^{2} + 1 \right)}} \left(- \frac{4 x^{2} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}}\right)^{2} + \frac{4 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{\left(x^{2} + 1\right) \sin{\left(x \right)}} + \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x^{2} \sin{\left(x \right)}}\right)$$
Tercera derivada [src]
                      /                                                     3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 \
             /     2\ |/                                           /     2\\      /                                           /     2\\ /                                               2                                           /     2\                          /     2\                                 /     2\\                                                       3                                        /     2\                            /     2\                                                                                      /     2\                               /     2\        2                           /     2\                                      /     2\                                   /     2\|
          log\1 + x / ||2*x*log(x*sin(x))   (x*cos(x) + sin(x))*log\1 + x /|      |2*x*log(x*sin(x))   (x*cos(x) + sin(x))*log\1 + x /| |  2*log(x*sin(x))   4*(x*cos(x) + sin(x))   4*x *log(x*sin(x))   (-2*cos(x) + x*sin(x))*log\1 + x /   (x*cos(x) + sin(x))*log\1 + x /   (x*cos(x) + sin(x))*cos(x)*log\1 + x /|   12*x*log(x*sin(x))   6*(-2*cos(x) + x*sin(x))   16*x *log(x*sin(x))   (x*cos(x) + sin(x))*log\1 + x /   (3*sin(x) + x*cos(x))*log\1 + x /   12*x*(x*cos(x) + sin(x))   6*(x*cos(x) + sin(x))*cos(x)   2*(x*cos(x) + sin(x))*log\1 + x /   2*(-2*cos(x) + x*sin(x))*log\1 + x /   2*cos (x)*(x*cos(x) + sin(x))*log\1 + x /   2*(-2*cos(x) + x*sin(x))*cos(x)*log\1 + x /   2*(x*cos(x) + sin(x))*cos(x)*log\1 + x /|
(x*sin(x))           *||----------------- + -------------------------------|  - 3*|----------------- + -------------------------------|*|- --------------- - --------------------- + ------------------ + ---------------------------------- + ------------------------------- + --------------------------------------| - ------------------ - ------------------------ + ------------------- + ------------------------------- - --------------------------------- - ------------------------ - ---------------------------- + --------------------------------- + ------------------------------------ + ----------------------------------------- + ------------------------------------------- + ----------------------------------------|
                      ||           2                    x*sin(x)           |      |           2                    x*sin(x)           | |            2          /     2\                         2                     x*sin(x)                            2                                        2                  |               2            /     2\                            3                    x*sin(x)                           x*sin(x)                           2                    /     2\    2                         3                                    2                                             3                                            2                                       2    2                  |
                      |\      1 + x                                        /      \      1 + x                                        / |       1 + x           \1 + x /*sin(x)          /     2\                                                         x *sin(x)                            x*sin (x)               |       /     2\             \1 + x /*sin(x)             /     2\                                                                                   /     2\                     \1 + x /*sin (x)                     x *sin(x)                            x *sin(x)                                 x*sin (x)                                    x*sin (x)                                   x *sin (x)               |
                      \                                                                                                                 \                                                \1 + x /                                                                                                                      /       \1 + x /                                         \1 + x /                                                                                   \1 + x / *sin(x)                                                                                                                                                                                                                                                   /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x^{2} + 1 \right)}} \left(\frac{16 x^{3} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2} \sin{\left(x \right)}} - \frac{12 x \log{\left(x \sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}}\right)^{3} - 3 \left(\frac{2 x \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}}\right) \left(\frac{4 x^{2} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{4 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{\left(x^{2} + 1\right) \sin{\left(x \right)}} - \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \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^{2} + 1 \right)}}{x^{2} \sin{\left(x \right)}}\right) - \frac{6 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{\left(x^{2} + 1\right) \sin{\left(x \right)}} - \frac{6 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\left(x^{2} + 1\right) \sin^{2}{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x^{2} + 1 \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^{2} + 1 \right)}}{x \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \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^{2} + 1 \right)}}{x \sin{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}}{x^{2} \sin^{2}{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x^{3} \sin{\left(x \right)}}\right)$$
Gráfico
Derivada de (x*sin(x))^(ln(x*x+1))