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(x-x^-1)^sinx

Derivada de (x-x^-1)^sinx

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

Gráfico:

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Solución

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

    Perola derivada


Respuesta:

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