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x^th(x)
Derivada de la función/ th(x)/ x^th(x)

Derivada de x^th(x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
 tanh(x)
x
xtanh⁡(x)x^{\tanh{\left(x \right)}} 
x^tanh(x)
Solución detallada

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

    Perola derivada

    (log⁡(tanh⁡(x))+1)tanh⁡tanh⁡(x)(x)\left(\log{\left(\tanh{\left(x \right)} \right)} + 1\right) \tanh^{\tanh{\left(x \right)}}{\left(x \right)}

Respuesta:

(log⁡(tanh⁡(x))+1)tanh⁡tanh⁡(x)(x)\left(\log{\left(\tanh{\left(x \right)} \right)} + 1\right) \tanh^{\tanh{\left(x \right)}}{\left(x \right)}

Gráfica
02468-8-6-4-2-101020-10
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 tanh(x) /tanh(x)   /        2   \       \
x       *|------- + \1 - tanh (x)/*log(x)|
         \   x                           /
xtanh⁡(x)((1−tanh⁡2(x))log⁡(x)+tanh⁡(x)x)x^{\tanh{\left(x \right)}} \left(\left(1 - \tanh^{2}{\left(x \right)}\right) \log{\left(x \right)} + \frac{\tanh{\left(x \right)}}{x}\right)
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Segunda derivada [src] 
         /                                  2               /         2   \                                   \
 tanh(x) |//         2   \          tanh(x)\    tanh(x)   2*\-1 + tanh (x)/     /         2   \               |
x       *||\-1 + tanh (x)/*log(x) - -------|  - ------- - ----------------- + 2*\-1 + tanh (x)/*log(x)*tanh(x)|
         |\                            x   /        2             x                                           |
         \                                         x                                                          /
xtanh⁡(x)(((tanh⁡2(x)−1)log⁡(x)−tanh⁡(x)x)2+2(tanh⁡2(x)−1)log⁡(x)tanh⁡(x)−2(tanh⁡2(x)−1)x−tanh⁡(x)x2)x^{\tanh{\left(x \right)}} \left(\left(\left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x \right)} - \frac{\tanh{\left(x \right)}}{x}\right)^{2} + 2 \left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x \right)} \tanh{\left(x \right)} - \frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right)}{x} - \frac{\tanh{\left(x \right)}}{x^{2}}\right)
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Tercera derivada [src] 
         /                                    3                    2                        /         2   \                                        /            /         2   \                                   \                                         /         2   \        \
 tanh(x) |  //         2   \          tanh(x)\      /         2   \           2*tanh(x)   3*\-1 + tanh (x)/     //         2   \          tanh(x)\ |tanh(x)   2*\-1 + tanh (x)/     /         2   \               |         2    /         2   \          6*\-1 + tanh (x)/*tanh(x)|
x       *|- |\-1 + tanh (x)/*log(x) - -------|  - 2*\-1 + tanh (x)/ *log(x) + --------- + ----------------- + 3*|\-1 + tanh (x)/*log(x) - -------|*|------- + ----------------- - 2*\-1 + tanh (x)/*log(x)*tanh(x)| - 4*tanh (x)*\-1 + tanh (x)/*log(x) + -------------------------|
         |  \                            x   /                                     3               2            \                            x   / |    2             x                                           |                                                   x            |
         \                                                                        x               x                                                \   x                                                          /                                                                /
xtanh⁡(x)(−((tanh⁡2(x)−1)log⁡(x)−tanh⁡(x)x)3+3((tanh⁡2(x)−1)log⁡(x)−tanh⁡(x)x)(−2(tanh⁡2(x)−1)log⁡(x)tanh⁡(x)+2(tanh⁡2(x)−1)x+tanh⁡(x)x2)−2(tanh⁡2(x)−1)2log⁡(x)−4(tanh⁡2(x)−1)log⁡(x)tanh⁡2(x)+6(tanh⁡2(x)−1)tanh⁡(x)x+3(tanh⁡2(x)−1)x2+2tanh⁡(x)x3)x^{\tanh{\left(x \right)}} \left(- \left(\left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x \right)} - \frac{\tanh{\left(x \right)}}{x}\right)^{3} + 3 \left(\left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x \right)} - \frac{\tanh{\left(x \right)}}{x}\right) \left(- 2 \left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x \right)} \tanh{\left(x \right)} + \frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right)}{x} + \frac{\tanh{\left(x \right)}}{x^{2}}\right) - 2 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2} \log{\left(x \right)} - 4 \left(\tanh^{2}{\left(x \right)} - 1\right) \log{\left(x \right)} \tanh^{2}{\left(x \right)} + \frac{6 \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)}}{x} + \frac{3 \left(\tanh^{2}{\left(x \right)} - 1\right)}{x^{2}} + \frac{2 \tanh{\left(x \right)}}{x^{3}}\right)
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Gráfico
Derivada de x^th(x)
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