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

Derivada de y=arctg(x)^x

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

Gráfico:

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Definida a trozos:

Solución

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-5050
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Primera derivada [src] 
    x    /       x                       \
atan (x)*|---------------- + log(atan(x))|
         |/     2\                       |
         \\1 + x /*atan(x)               /
(x(x2+1)atan⁡(x)+log⁡(atan⁡(x)))atan⁡x(x)\left(\frac{x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \log{\left(\operatorname{atan}{\left(x \right)} \right)}\right) \operatorname{atan}^{x}{\left(x \right)}
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Segunda derivada [src] 
         /                                              2                    \
         |                                           2*x            x        |
         |                                     -2 + ------ + ----------------|
         |                                 2             2   /     2\        |
    x    |/       x                       \         1 + x    \1 + x /*atan(x)|
atan (x)*||---------------- + log(atan(x))|  - ------------------------------|
         ||/     2\                       |           /     2\               |
         \\\1 + x /*atan(x)               /           \1 + x /*atan(x)       /
((x(x2+1)atan⁡(x)+log⁡(atan⁡(x)))2−2x2x2+1+x(x2+1)atan⁡(x)−2(x2+1)atan⁡(x))atan⁡x(x)\left(\left(\frac{x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \log{\left(\operatorname{atan}{\left(x \right)} \right)}\right)^{2} - \frac{\frac{2 x^{2}}{x^{2} + 1} + \frac{x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - 2}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}\right) \operatorname{atan}^{x}{\left(x \right)}
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Tercera derivada [src] 
         /                                                          3                                 2                                             /         2                    \\
         |                                               3       8*x            2*x                6*x            /       x                       \ |      2*x            x        ||
         |                                     -8*x - ------- + ------ + ----------------- + ----------------   3*|---------------- + log(atan(x))|*|-2 + ------ + ----------------||
         |                                 3          atan(x)        2   /     2\     2      /     2\             |/     2\                       | |          2   /     2\        ||
    x    |/       x                       \                     1 + x    \1 + x /*atan (x)   \1 + x /*atan(x)     \\1 + x /*atan(x)               / \     1 + x    \1 + x /*atan(x)/|
atan (x)*||---------------- + log(atan(x))|  + -------------------------------------------------------------- - --------------------------------------------------------------------|
         ||/     2\                       |                                  2                                                            /     2\                                  |
         |\\1 + x /*atan(x)               /                          /     2\                                                             \1 + x /*atan(x)                          |
         \                                                           \1 + x / *atan(x)                                                                                              /
((x(x2+1)atan⁡(x)+log⁡(atan⁡(x)))3−3(x(x2+1)atan⁡(x)+log⁡(atan⁡(x)))(2x2x2+1+x(x2+1)atan⁡(x)−2)(x2+1)atan⁡(x)+8x3x2+1+6x2(x2+1)atan⁡(x)−8x+2x(x2+1)atan⁡2(x)−3atan⁡(x)(x2+1)2atan⁡(x))atan⁡x(x)\left(\left(\frac{x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \log{\left(\operatorname{atan}{\left(x \right)} \right)}\right)^{3} - \frac{3 \left(\frac{x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \log{\left(\operatorname{atan}{\left(x \right)} \right)}\right) \left(\frac{2 x^{2}}{x^{2} + 1} + \frac{x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - 2\right)}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\frac{8 x^{3}}{x^{2} + 1} + \frac{6 x^{2}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - 8 x + \frac{2 x}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}} - \frac{3}{\operatorname{atan}{\left(x \right)}}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}}\right) \operatorname{atan}^{x}{\left(x \right)}
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Gráfico
Derivada de y=arctg(x)^x
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