Derivada de y=(arctan3x)^ln

Ha introducido [src]

    log(x)     
atan      (3*x)

\operatorname{atan}^{\log{\left(x \right)}}{\left(3 x \right)}

atan(3*x)^log(x)

Solución detallada

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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

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Trazar el gráfico f'(x)

Primera derivada [src]

    log(x)      /log(atan(3*x))         3*log(x)      \
atan      (3*x)*|-------------- + --------------------|
                |      x          /       2\          |
                \                 \1 + 9*x /*atan(3*x)/

\left(\frac{3 \log{\left(x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(3 x \right)}

Simplificar

Segunda derivada [src]

                /                                       2                                                                                           \
    log(x)      |/log(atan(3*x))         3*log(x)      \    log(atan(3*x))          9*log(x)                    6                   54*x*log(x)     |
atan      (3*x)*||-------------- + --------------------|  - -------------- - ---------------------- + ---------------------- - ---------------------|
                ||      x          /       2\          |           2                   2                /       2\                       2          |
                |\                 \1 + 9*x /*atan(3*x)/          x          /       2\      2        x*\1 + 9*x /*atan(3*x)   /       2\           |
                \                                                            \1 + 9*x / *atan (3*x)                            \1 + 9*x / *atan(3*x)/

\left(- \frac{54 x \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + \left(\frac{3 \log{\left(x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x}\right)^{2} - \frac{9 \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(3 x \right)}} + \frac{6}{x \left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x^{2}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(3 x \right)}

Simplificar

Tercera derivada [src]

                /                                       3                                                                                                                                                                                                                                                                                                                              2          \
    log(x)      |/log(atan(3*x))         3*log(x)      \             162              /log(atan(3*x))         3*log(x)      \ /log(atan(3*x))             6                     9*log(x)               54*x*log(x)     \   2*log(atan(3*x))         54*log(x)                    27                         9                    54*log(x)               486*x*log(x)            1944*x *log(x)   |
atan      (3*x)*||-------------- + --------------------|  - --------------------- - 3*|-------------- + --------------------|*|-------------- - ---------------------- + ---------------------- + ---------------------| + ---------------- - --------------------- - ------------------------ - ----------------------- + ---------------------- + ---------------------- + ---------------------|
                ||      x          /       2\          |              2               |      x          /       2\          | |       2           /       2\                       2                        2          |           3                    2                         2               2 /       2\                       3                        3                        3          |
                |\                 \1 + 9*x /*atan(3*x)/    /       2\                \                 \1 + 9*x /*atan(3*x)/ |      x          x*\1 + 9*x /*atan(3*x)   /       2\      2        /       2\           |          x           /       2\                /       2\      2        x *\1 + 9*x /*atan(3*x)   /       2\      3        /       2\      2        /       2\           |
                \                                           \1 + 9*x / *atan(3*x)                                             \                                          \1 + 9*x / *atan (3*x)   \1 + 9*x / *atan(3*x)/                      \1 + 9*x / *atan(3*x)   x*\1 + 9*x / *atan (3*x)                             \1 + 9*x / *atan (3*x)   \1 + 9*x / *atan (3*x)   \1 + 9*x / *atan(3*x)/

\left(\frac{1944 x^{2} \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{3} \operatorname{atan}{\left(3 x \right)}} + \frac{486 x \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(3 x \right)}} + \left(\frac{3 \log{\left(x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{3 \log{\left(x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x}\right) \left(\frac{54 x \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + \frac{9 \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(3 x \right)}} - \frac{6}{x \left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x^{2}}\right) - \frac{54 \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} - \frac{162}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + \frac{54 \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(3 x \right)}} - \frac{27}{x \left(9 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(3 x \right)}} - \frac{9}{x^{2} \left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x^{3}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(3 x \right)}

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Gráfico

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Derivada de y=(arctan3x)^ln

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