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Derivada de la función/ x*sin/ (1/x)/ (x^2)/ (x*sin(1/x))^(x^2)

Derivada de (x*sin(1/x))^(x^2)

Solución

Ha introducido [src]

          / 2\
          \x /
/     /1\\    
|x*sin|-||    
\     \x//

\left(x \sin{\left(\frac{1}{x} \right)}\right)^{x^{2}}

(x*sin(1/x))^(x^2)

Solución detallada

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

Perola derivada

$\left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}}$

Respuesta:

$\left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}}$

Primera derivada [src]

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

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

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Segunda derivada [src]

               /                                                                 2                                                     \
               |                            /                       /1\         \      /     /1\         \   /     /1\         \       |
               |                            |                    cos|-|         |      |  cos|-|         |   |  cos|-|         |       |
          / 2\ |                            |                       \x/      /1\|      |     \x/      /1\|   |     \x/      /1\|    /1\|
          \x / |                            |                  - ------ + sin|-||    3*|- ------ + sin|-||   |- ------ + sin|-||*cos|-||
/     /1\\     |  1         /     /1\\    2 |     /     /1\\       x         \x/|      \    x         \x//   \    x         \x//    \x/|
|x*sin|-||    *|- -- + 2*log|x*sin|-|| + x *|2*log|x*sin|-|| + -----------------|  + --------------------- + --------------------------|
\     \x//     |   2        \     \x//      |     \     \x//            /1\     |               /1\                       2/1\         |
               |  x                         |                        sin|-|     |            sin|-|                  x*sin |-|         |
               \                            \                           \x/     /               \x/                        \x/         /

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

Simplificar

Tercera derivada [src]

               /         /     /1\         \        /1\                          /     /1\         \                    /     /1\         \                                                                                                                                                                      \
               |         |  cos|-|         |     cos|-|                          |  cos|-|         |                    |  cos|-|         |                                                                                                                                                                      |
               |         |     \x/      /1\|        \x/      /1\        /1\      |     \x/      /1\|    /1\        2/1\ |     \x/      /1\|                                                                                                                                                                      |
               |       2*|- ------ + sin|-||   - ------ + sin|-|     cos|-|    2*|- ------ + sin|-||*cos|-|   2*cos |-|*|- ------ + sin|-||                                           3                                                                                                                          |
               |  1      \    x         \x//       x         \x/        \x/      \    x         \x//    \x/         \x/ \    x         \x//      /                       /1\         \        /                       /1\         \ /                           /     /1\         \   /     /1\         \       \|
               |- -- + --------------------- + ----------------- - --------- + ---------------------------- + -----------------------------      |                    cos|-|         |        |                    cos|-|         | |                           |  cos|-|         |   |  cos|-|         |       ||
          / 2\ |   2              /1\               2    /1\        3    /1\                 2/1\                        2    3/1\               |                       \x/      /1\|        |                       \x/      /1\| |                           |     \x/      /1\|   |     \x/      /1\|    /1\||
          \x / |  x            sin|-|              x *sin|-|       x *sin|-|            x*sin |-|                       x *sin |-|               |                  - ------ + sin|-||        |                  - ------ + sin|-|| |                         3*|- ------ + sin|-||   |- ------ + sin|-||*cos|-|||
/     /1\\     |                  \x/                    \x/             \x/                  \x/                              \x/             3 |     /     /1\\       x         \x/|        |     /     /1\\       x         \x/| |  1         /     /1\\     \    x         \x//   \    x         \x//    \x/||
|x*sin|-||    *|--------------------------------------------------------------------------------------------------------------------------- + x *|2*log|x*sin|-|| + -----------------|  + 3*x*|2*log|x*sin|-|| + -----------------|*|- -- + 2*log|x*sin|-|| + --------------------- + --------------------------||
\     \x//     |                                                             x                                                                   |     \     \x//            /1\     |        |     \     \x//            /1\     | |   2        \     \x//              /1\                       2/1\         ||
               |                                                                                                                                 |                        sin|-|     |        |                        sin|-|     | |  x                              sin|-|                  x*sin |-|         ||
               \                                                                                                                                 \                           \x/     /        \                           \x/     / \                                    \x/                        \x/         //

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

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Gráfico

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Derivada de (x*sin(1/x))^(x^2)

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