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Expresiones idénticas
y=sin(x)^(tg(uno /x))
y es igual a seno de (x) en el grado (tg(1 dividir por x))
y es igual a seno de (x) en el grado (tg(uno dividir por x))
y=sin(x)(tg(1/x))
y=sinxtg1/x
y=sinx^tg1/x
y=sin(x)^(tg(1 dividir por x))
Expresiones semejantes
y=sinx^(tg(1/x))

Derivada de la función/ (1/x)/ y=sin/ sin(x)/ y=sin(x)^(tg(1/x))

Derivada de y=sin(x)^(tg(1/x))

Solución

Ha introducido [src]

           /1\
        tan|-|
           \x/
(sin(x))

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

sin(x)^tan(1/x)

Solución detallada

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

Perola derivada

$\left(\log{\left(\tan{\left(\frac{1}{x} \right)} \right)} + 1\right) \tan^{\tan{\left(\frac{1}{x} \right)}}{\left(\frac{1}{x} \right)}$

Respuesta:

$\left(\log{\left(\tan{\left(\frac{1}{x} \right)} \right)} + 1\right) \tan^{\tan{\left(\frac{1}{x} \right)}}{\left(\frac{1}{x} \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

               /                                           2                                                                                                                      \
           /1\ |/          /1\   /       2/1\\            \                2       /1\     /       2/1\\                 /       2/1\\            /       2/1\\                /1\|
        tan|-| ||cos(x)*tan|-|   |1 + tan |-||*log(sin(x))|             cos (x)*tan|-|   2*|1 + tan |-||*log(sin(x))   2*|1 + tan |-||*cos(x)   2*|1 + tan |-||*log(sin(x))*tan|-||
           \x/ ||          \x/   \        \x//            |       /1\              \x/     \        \x//                 \        \x//            \        \x//                \x/|
(sin(x))      *||------------- - -------------------------|  - tan|-| - -------------- + --------------------------- - ---------------------- + ----------------------------------|
               ||    sin(x)                   2           |       \x/         2                        3                      2                                  4                |
               \\                            x            /                sin (x)                    x                      x *sin(x)                          x                 /

\left(\left(\frac{\cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\sin{\left(x \right)}} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{2}}\right)^{2} - \tan{\left(\frac{1}{x} \right)} - \frac{\cos^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{3}} + \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan{\left(\frac{1}{x} \right)}}{x^{4}}\right) \sin^{\tan{\left(\frac{1}{x} \right)}}{\left(x \right)}

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Tercera derivada [src]

               /                                           3                                                                                                                                                                                                                                        2                                                                                                                                                                                                                \
           /1\ |/          /1\   /       2/1\\            \      /          /1\   /       2/1\\            \ /   2       /1\     /       2/1\\                 /       2/1\\                /1\     /       2/1\\                \     /       2/1\\     /       2/1\\                 /       2/1\\                     3       /1\               /1\      /       2/1\\                /1\        2/1\ /       2/1\\                    2    /       2/1\\     /       2/1\\            /       2/1\\           /1\|
        tan|-| ||cos(x)*tan|-|   |1 + tan |-||*log(sin(x))|      |cos(x)*tan|-|   |1 + tan |-||*log(sin(x))| |cos (x)*tan|-|   2*|1 + tan |-||*log(sin(x))   2*|1 + tan |-||*log(sin(x))*tan|-|   2*|1 + tan |-||*cos(x)         |   3*|1 + tan |-||   6*|1 + tan |-||*log(sin(x))   2*|1 + tan |-|| *log(sin(x))   2*cos (x)*tan|-|   2*cos(x)*tan|-|   12*|1 + tan |-||*log(sin(x))*tan|-|   4*tan |-|*|1 + tan |-||*log(sin(x))   3*cos (x)*|1 + tan |-||   6*|1 + tan |-||*cos(x)   6*|1 + tan |-||*cos(x)*tan|-||
           \x/ ||          \x/   \        \x//            |      |          \x/   \        \x//            | |           \x/     \        \x//                 \        \x//                \x/     \        \x//             /1\|     \        \x//     \        \x//                 \        \x//                             \x/               \x/      \        \x//                \x/         \x/ \        \x//                         \        \x//     \        \x//            \        \x//           \x/|
(sin(x))      *||------------- - -------------------------|  - 3*|------------- - -------------------------|*|-------------- - --------------------------- - ---------------------------------- + ---------------------- + tan|-|| + --------------- - --------------------------- - ---------------------------- + ---------------- + --------------- - ----------------------------------- - ----------------------------------- + ----------------------- + ---------------------- + -----------------------------|
               ||    sin(x)                   2           |      |    sin(x)                   2           | |      2                        3                                4                          2                    \x/|           2                       4                             6                       3                sin(x)                         5                                     6                           2    2                   3                            4                 |
               \\                            x            /      \                            x            / \   sin (x)                    x                                x                          x *sin(x)                /          x                       x                             x                     sin (x)                                           x                                     x                           x *sin (x)               x *sin(x)                    x *sin(x)          /

\left(\left(\frac{\cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\sin{\left(x \right)}} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{2}}\right)^{3} - 3 \left(\frac{\cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\sin{\left(x \right)}} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{2}}\right) \left(\tan{\left(\frac{1}{x} \right)} + \frac{\cos^{2}{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{3}} - \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan{\left(\frac{1}{x} \right)}}{x^{4}}\right) + \frac{2 \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{\sin^{3}{\left(x \right)}} + \frac{3 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x^{2}} + \frac{3 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \cos^{2}{\left(x \right)}}{x^{2} \sin^{2}{\left(x \right)}} + \frac{6 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \cos{\left(x \right)}}{x^{3} \sin{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)}}{x^{4}} + \frac{6 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \cos{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{x^{4} \sin{\left(x \right)}} - \frac{12 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan{\left(\frac{1}{x} \right)}}{x^{5}} - \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)^{2} \log{\left(\sin{\left(x \right)} \right)}}{x^{6}} - \frac{4 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan^{2}{\left(\frac{1}{x} \right)}}{x^{6}}\right) \sin^{\tan{\left(\frac{1}{x} \right)}}{\left(x \right)}

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Gráfico

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Expresiones idénticas

Expresiones semejantes

Derivada de y=sin(x)^(tg(1/x))

Gráfico:

Definida a trozos:

Solución