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x^tg(1/x)
Derivada de la función/ (1/x)/ x^tg(1/x)

Derivada de x^tg(1/x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /1\
 tan|-|
    \x/
x
xtan⁡(1x)x^{\tan{\left(\frac{1}{x} \right)}} 
x^tan(1/x)
Solución detallada

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

    Perola derivada

    (log⁡(tan⁡(1x))+1)tan⁡tan⁡(1x)(1x)\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:

(log⁡(tan⁡(1x))+1)tan⁡tan⁡(1x)(1x)\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
02468-8-6-4-2-1010-100100
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Trazar el gráfico f'(x)
Primera derivada [src] 
    /1\ /   /1\   /       2/1\\       \
 tan|-| |tan|-|   |1 + tan |-||*log(x)|
    \x/ |   \x/   \        \x//       |
x      *|------ - --------------------|
        |  x                2         |
        \                  x          /
xtan⁡(1x)(tan⁡(1x)x−(tan⁡2(1x)+1)log⁡(x)x2)x^{\tan{\left(\frac{1}{x} \right)}} \left(\frac{\tan{\left(\frac{1}{x} \right)}}{x} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)}}{x^{2}}\right)
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Segunda derivada [src] 
        /                                 2                                                                                    \
    /1\ |/  /       2/1\\                \               /       2/1\\     /       2/1\\            /       2/1\\           /1\|
 tan|-| ||  |1 + tan |-||*log(x)         |             2*|1 + tan |-||   2*|1 + tan |-||*log(x)   2*|1 + tan |-||*log(x)*tan|-||
    \x/ ||  \        \x//             /1\|       /1\     \        \x//     \        \x//            \        \x//           \x/|
x      *||- -------------------- + tan|-||  - tan|-| - --------------- + ---------------------- + -----------------------------|
        |\           x                \x//       \x/          x                    x                             2             |
        \                                                                                                       x              /
--------------------------------------------------------------------------------------------------------------------------------
                                                                2                                                               
                                                               x
xtan⁡(1x)((tan⁡(1x)−(tan⁡2(1x)+1)log⁡(x)x)2−tan⁡(1x)+2(tan⁡2(1x)+1)log⁡(x)x−2(tan⁡2(1x)+1)x+2(tan⁡2(1x)+1)log⁡(x)tan⁡(1x)x2)x2\frac{x^{\tan{\left(\frac{1}{x} \right)}} \left(\left(\tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)}}{x}\right)^{2} - \tan{\left(\frac{1}{x} \right)} + \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)}}{x} - \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x} + \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{x^{2}}\right)}{x^{2}}
Simplificar
Tercera derivada [src] 
        /                                 3                                                                                                                                                                                                  2                                                                                                  \
    /1\ |/  /       2/1\\                \                 /  /       2/1\\                \ /  /       2/1\\     /       2/1\\            /       2/1\\           /1\         \     /       2/1\\     /       2/1\\            /       2/1\\             /       2/1\\    /1\      /       2/1\\           /1\        2/1\ /       2/1\\       |
 tan|-| ||  |1 + tan |-||*log(x)         |                 |  |1 + tan |-||*log(x)         | |2*|1 + tan |-||   2*|1 + tan |-||*log(x)   2*|1 + tan |-||*log(x)*tan|-|         |   9*|1 + tan |-||   6*|1 + tan |-||*log(x)   2*|1 + tan |-|| *log(x)   6*|1 + tan |-||*tan|-|   12*|1 + tan |-||*log(x)*tan|-|   4*tan |-|*|1 + tan |-||*log(x)|
    \x/ ||  \        \x//             /1\|         /1\     |  \        \x//             /1\| |  \        \x//     \        \x//            \        \x//           \x/      /1\|     \        \x//     \        \x//            \        \x//             \        \x//    \x/      \        \x//           \x/         \x/ \        \x//       |
x      *||- -------------------- + tan|-||  + 2*tan|-| - 3*|- -------------------- + tan|-||*|--------------- - ---------------------- - ----------------------------- + tan|-|| + --------------- - ---------------------- - ----------------------- + ---------------------- - ------------------------------ - ------------------------------|
        |\           x                \x//         \x/     \           x                \x// |       x                    x                             2                   \x/|          x                    x                          3                        2                            2                                3              |
        \                                                                                    \                                                         x                       /                                                         x                        x                            x                                x               /
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                                                                                                                                                                         3                                                                                                                                                                       
                                                                                                                                                                        x
xtan⁡(1x)((tan⁡(1x)−(tan⁡2(1x)+1)log⁡(x)x)3−3(tan⁡(1x)−(tan⁡2(1x)+1)log⁡(x)x)(tan⁡(1x)−2(tan⁡2(1x)+1)log⁡(x)x+2(tan⁡2(1x)+1)x−2(tan⁡2(1x)+1)log⁡(x)tan⁡(1x)x2)+2tan⁡(1x)−6(tan⁡2(1x)+1)log⁡(x)x+9(tan⁡2(1x)+1)x−12(tan⁡2(1x)+1)log⁡(x)tan⁡(1x)x2+6(tan⁡2(1x)+1)tan⁡(1x)x2−2(tan⁡2(1x)+1)2log⁡(x)x3−4(tan⁡2(1x)+1)log⁡(x)tan⁡2(1x)x3)x3\frac{x^{\tan{\left(\frac{1}{x} \right)}} \left(\left(\tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)}}{x}\right)^{3} - 3 \left(\tan{\left(\frac{1}{x} \right)} - \frac{\left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)}}{x}\right) \left(\tan{\left(\frac{1}{x} \right)} - \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)}}{x} + \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x} - \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{x^{2}}\right) + 2 \tan{\left(\frac{1}{x} \right)} - \frac{6 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)}}{x} + \frac{9 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)}{x} - \frac{12 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)} \tan{\left(\frac{1}{x} \right)}}{x^{2}} + \frac{6 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \tan{\left(\frac{1}{x} \right)}}{x^{2}} - \frac{2 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right)^{2} \log{\left(x \right)}}{x^{3}} - \frac{4 \left(\tan^{2}{\left(\frac{1}{x} \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(\frac{1}{x} \right)}}{x^{3}}\right)}{x^{3}}
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Gráfico
Derivada de x^tg(1/x)
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