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Derivada de:
Derivada de 6/x
Derivada de 2*sqrt(x)
Derivada de e^(5*x)
Derivada de 1+x
Expresiones idénticas
(atan(x))^(log(x))
( arco tangente de gente de (x)) en el grado ( logaritmo de (x))
(atan(x))(log(x))
atanxlogx
atanx^logx
Expresiones semejantes
(arctan(x))^(log(x))
(arctanx)^(log(x))
Expresiones con funciones
Arcotangente arctan
atan(x/2)
atan(t)
atan(x)*sqrt(x^2-1)
atan(log(x))+log(atan(x))
atan(x/sqrt(3))
Logaritmo log
log(x^2)
log
log(x)/sqrt(x)
log(x+3)
log(x^2*e^x)

Derivada de la función/ log(x)/ tan(x)/ (atan(x))^(log(x))

Derivada de (atan(x))^(log(x))

Solución

Ha introducido [src]

    log(x)   
atan      (x)

$$\operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$

atan(x)^log(x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

    log(x)    /log(atan(x))        log(x)     \
atan      (x)*|------------ + ----------------|
              |     x         /     2\        |
              \               \1 + x /*atan(x)/

$$\left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$

Simplificar

Segunda derivada [src]

              /                                 2                                                                             \
    log(x)    |/log(atan(x))        log(x)     \    log(atan(x))         log(x)                 2                2*x*log(x)   |
atan      (x)*||------------ + ----------------|  - ------------ - ------------------ + ------------------ - -----------------|
              ||     x         /     2\        |          2                2              /     2\                   2        |
              |\               \1 + x /*atan(x)/         x         /     2\      2      x*\1 + x /*atan(x)   /     2\         |
              \                                                    \1 + x / *atan (x)                        \1 + x / *atan(x)/

$$\left(- \frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right)^{2} - \frac{\log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} + \frac{2}{x \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x^{2}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$

Simplificar

Tercera derivada [src]

              /                                 3                                                                                                                                                                                                                                                                            2          \
    log(x)    |/log(atan(x))        log(x)     \            6             /log(atan(x))        log(x)     \ /log(atan(x))         log(x)                 2                2*x*log(x)   \   2*log(atan(x))            3                      3                 2*log(x)            2*log(x)            6*x*log(x)          8*x *log(x)   |
atan      (x)*||------------ + ----------------|  - ----------------- - 3*|------------ + ----------------|*|------------ + ------------------ - ------------------ + -----------------| + -------------- - -------------------- - ------------------- - ----------------- + ------------------ + ------------------ + -----------------|
              ||     x         /     2\        |            2             |     x         /     2\        | |      2                2              /     2\                   2        |          3                   2             2 /     2\                   2                   3                    3                    3        |
              |\               \1 + x /*atan(x)/    /     2\              \               \1 + x /*atan(x)/ |     x         /     2\      2      x*\1 + x /*atan(x)   /     2\         |         x            /     2\      2      x *\1 + x /*atan(x)   /     2\            /     2\      3      /     2\      2      /     2\         |
              \                                     \1 + x / *atan(x)                                       \               \1 + x / *atan (x)                        \1 + x / *atan(x)/                    x*\1 + x / *atan (x)                         \1 + x / *atan(x)   \1 + x / *atan (x)   \1 + x / *atan (x)   \1 + x / *atan(x)/

$$\left(\frac{8 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}{\left(x \right)}} + \frac{6 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right) \left(\frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} - \frac{2}{x \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x^{2}}\right) - \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} - \frac{6}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(x \right)}} - \frac{3}{x \left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} - \frac{3}{x^{2} \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x^{3}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$

Simplificar

Gráfico

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Expresiones idénticas

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Expresiones con funciones

Derivada de (atan(x))^(log(x))

Gráfico:

Definida a trozos:

Solución