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(x-x^-2)^sinx

Derivada de (x-x^-2)^sinx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
        sin(x)
/    1 \      
|x - --|      
|     2|      
\    x /      
$$\left(x - \frac{1}{x^{2}}\right)^{\sin{\left(x \right)}}$$
(x - 1/x^2)^sin(x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
               /                     /    2 \       \
               |                     |1 + --|*sin(x)|
        sin(x) |                     |     3|       |
/    1 \       |          /    1 \   \    x /       |
|x - --|      *|cos(x)*log|x - --| + ---------------|
|     2|       |          |     2|            1     |
\    x /       |          \    x /        x - --    |
               |                               2    |
               \                              x     /
$$\left(x - \frac{1}{x^{2}}\right)^{\sin{\left(x \right)}} \left(\frac{\left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)}\right)$$
Segunda derivada [src]
               /                                      2                                2                                         \
               |/                     /    2 \       \                         /    2 \                           /    2 \       |
               ||                     |1 + --|*sin(x)|                         |1 + --| *sin(x)                 2*|1 + --|*cos(x)|
        sin(x) ||                     |     3|       |                         |     3|                           |     3|       |
/    1 \       ||          /    1 \   \    x /       |       /    1 \          \    x /             6*sin(x)      \    x /       |
|x - --|      *||cos(x)*log|x - --| + ---------------|  - log|x - --|*sin(x) - ---------------- - ----------- + -----------------|
|     2|       ||          |     2|            1     |       |     2|                     2        4 /    1 \             1      |
\    x /       ||          \    x /        x - --    |       \    x /             /    1 \        x *|x - --|         x - --     |
               ||                               2    |                            |x - --|           |     2|              2     |
               |\                              x     /                            |     2|           \    x /             x      |
               \                                                                  \    x /                                       /
$$\left(x - \frac{1}{x^{2}}\right)^{\sin{\left(x \right)}} \left(- \frac{\left(1 + \frac{2}{x^{3}}\right)^{2} \sin{\left(x \right)}}{\left(x - \frac{1}{x^{2}}\right)^{2}} + \frac{2 \left(1 + \frac{2}{x^{3}}\right) \cos{\left(x \right)}}{x - \frac{1}{x^{2}}} + \left(\frac{\left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)}\right)^{2} - \log{\left(x - \frac{1}{x^{2}} \right)} \sin{\left(x \right)} - \frac{6 \sin{\left(x \right)}}{x^{4} \left(x - \frac{1}{x^{2}}\right)}\right)$$
Tercera derivada [src]
               /                                      3                                                                 /                             2                                         \                           2                                        3                                          \
               |/                     /    2 \       \                           /                     /    2 \       \ |                     /    2 \             /    2 \                     |                   /    2 \             /    2 \            /    2 \                            /    2 \       |
               ||                     |1 + --|*sin(x)|                           |                     |1 + --|*sin(x)| |                     |1 + --| *sin(x)   2*|1 + --|*cos(x)              |                 3*|1 + --| *cos(x)   3*|1 + --|*sin(x)   2*|1 + --| *sin(x)                 18*|1 + --|*sin(x)|
        sin(x) ||                     |     3|       |                           |                     |     3|       | |                     |     3|             |     3|                     |                   |     3|             |     3|            |     3|                            |     3|       |
/    1 \       ||          /    1 \   \    x /       |              /    1 \     |          /    1 \   \    x /       | |   /    1 \          \    x /             \    x /            6*sin(x) |    18*cos(x)      \    x /             \    x /            \    x /            24*sin(x)       \    x /       |
|x - --|      *||cos(x)*log|x - --| + ---------------|  - cos(x)*log|x - --| - 3*|cos(x)*log|x - --| + ---------------|*|log|x - --|*sin(x) + ---------------- - ----------------- + -----------| - ----------- - ------------------ - ----------------- + ------------------ + ----------- + ------------------|
|     2|       ||          |     2|            1     |              |     2|     |          |     2|            1     | |   |     2|                     2                 1          4 /    1 \|    4 /    1 \               2                  1                     3         5 /    1 \                 2   |
\    x /       ||          \    x /        x - --    |              \    x /     |          \    x /        x - --    | |   \    x /             /    1 \              x - --        x *|x - --||   x *|x - --|       /    1 \               x - --            /    1 \         x *|x - --|       4 /    1 \    |
               ||                               2    |                           |                               2    | |                        |x - --|                   2           |     2||      |     2|       |x - --|                    2            |x - --|            |     2|      x *|x - --|    |
               |\                              x     /                           \                              x     / |                        |     2|                  x            \    x /|      \    x /       |     2|                   x             |     2|            \    x /         |     2|    |
               \                                                                                                        \                        \    x /                                       /                     \    x /                                 \    x /                             \    x /    /
$$\left(x - \frac{1}{x^{2}}\right)^{\sin{\left(x \right)}} \left(\frac{2 \left(1 + \frac{2}{x^{3}}\right)^{3} \sin{\left(x \right)}}{\left(x - \frac{1}{x^{2}}\right)^{3}} - \frac{3 \left(1 + \frac{2}{x^{3}}\right)^{2} \cos{\left(x \right)}}{\left(x - \frac{1}{x^{2}}\right)^{2}} - \frac{3 \left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \left(\frac{\left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)}\right)^{3} - 3 \left(\frac{\left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)}\right) \left(\frac{\left(1 + \frac{2}{x^{3}}\right)^{2} \sin{\left(x \right)}}{\left(x - \frac{1}{x^{2}}\right)^{2}} - \frac{2 \left(1 + \frac{2}{x^{3}}\right) \cos{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \sin{\left(x \right)} + \frac{6 \sin{\left(x \right)}}{x^{4} \left(x - \frac{1}{x^{2}}\right)}\right) - \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)} + \frac{18 \left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x^{4} \left(x - \frac{1}{x^{2}}\right)^{2}} - \frac{18 \cos{\left(x \right)}}{x^{4} \left(x - \frac{1}{x^{2}}\right)} + \frac{24 \sin{\left(x \right)}}{x^{5} \left(x - \frac{1}{x^{2}}\right)}\right)$$
Gráfico
Derivada de (x-x^-2)^sinx