Derivada de y=(x^e)^arcctg(x)

Ha introducido [src]

    acot(x)
/ E\       
\x /

$$\left(x^{e}\right)^{\operatorname{acot}{\left(x \right)}}$$

(x^E)^acot(x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

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

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

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Tercera derivada [src]

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

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

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Gráfico

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Expresiones idénticas

Derivada de y=(x^e)^arcctg(x)

Gráfico:

Definida a trozos:

Solución