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y=(arccosx)^ln^2x
y es igual a (arc coseno de x) en el grado ln al cuadrado x
y=(arccosx)ln2x
y=arccosxln2x
y=(arccosx)^ln²x
y=(arccosx) en el grado ln en el grado 2x
y=arccosx^ln^2x
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ln
ln(x/5)
ln(×)
ln(x+10)^10
ln(arcsinx)
ln(x+a)

Derivada de la función/ ln^2x/ arccos/ y=(arccosx)^ln^2x

Derivada de y=(arccosx)^ln^2x

Solución

Ha introducido [src]

            2   
         log (x)
(acos(x))

\operatorname{acos}^{\log{\left(x \right)}^{2}}{\left(x \right)}

acos(x)^(log(x)^2)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

            2    /                                        2                                    2                                              2                                \
         log (x) |/  2*log(acos(x))          log(x)      \     2      2*log(acos(x))        log (x)         2*log(x)*log(acos(x))        x*log (x)               4*log(x)      |
(acos(x))       *||- -------------- + -------------------| *log (x) + -------------- + ------------------ - --------------------- - ------------------- - ---------------------|
                 ||        x             ________        |                   2         /      2\     2                 2                    3/2                ________        |
                 ||                     /      2         |                  x          \-1 + x /*acos (x)             x             /     2\                  /      2         |
                 \\                   \/  1 - x  *acos(x)/                                                                          \1 - x /   *acos(x)   x*\/  1 - x  *acos(x)/

\left(- \frac{x \log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x}\right)^{2} \log{\left(x \right)}^{2} + \frac{\log{\left(x \right)}^{2}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{4 \log{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(x \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2}} + \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2}}\right) \operatorname{acos}^{\log{\left(x \right)}^{2}}{\left(x \right)}

Simplificar

Tercera derivada [src]

            2    /                                          3                                     2                                                                     2                                                       /                           2                                              2                                \                                             2                 2    2                                                      \
         log (x) |  /  2*log(acos(x))          log(x)      \     3      6*log(acos(x))         log (x)                   6                    6*log(x)             2*log (x)           /  2*log(acos(x))          log(x)      \ |  2*log(acos(x))        log (x)         2*log(x)*log(acos(x))        x*log (x)               4*log(x)      |          4*log(x)*log(acos(x))       3*x*log (x)           3*x *log (x)            6*log(x)                6*log(x)       |
(acos(x))       *|- |- -------------- + -------------------| *log (x) - -------------- - ------------------- - ---------------------- - ------------------- - -------------------- + 3*|- -------------- + -------------------|*|- -------------- - ------------------ + --------------------- + ------------------- + ---------------------|*log(x) + --------------------- - ------------------- - ------------------- + -------------------- + ----------------------|
                 |  |        x             ________        |                   3                 3/2                 ________                   3/2                   3/2              |        x             ________        | |         2         /      2\     2                 2                    3/2                ________        |                     3                     2                    5/2             /      2\     2            ________        |
                 |  |                     /      2         |                  x          /     2\               2   /      2            /     2\              /     2\        3        |                     /      2         | |        x          \-1 + x /*acos (x)             x             /     2\                  /      2         |                    x             /      2\      2      /     2\              x*\-1 + x /*acos (x)    2   /      2         |
                 \  \                   \/  1 - x  *acos(x)/                             \1 - x /   *acos(x)   x *\/  1 - x  *acos(x)   \1 - x /   *acos(x)   \1 - x /   *acos (x)     \                   \/  1 - x  *acos(x)/ \                                                                \1 - x /   *acos(x)   x*\/  1 - x  *acos(x)/                                  \-1 + x / *acos (x)   \1 - x /   *acos(x)                          x *\/  1 - x  *acos(x)/

\left(- \frac{3 x^{2} \log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{acos}{\left(x \right)}} - \frac{3 x \log{\left(x \right)}^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(x \right)}} - \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x}\right)^{3} \log{\left(x \right)}^{3} + 3 \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x}\right) \left(\frac{x \log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{\log{\left(x \right)}^{2}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} + \frac{4 \log{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + \frac{2 \log{\left(x \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2}} - \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2}}\right) \log{\left(x \right)} - \frac{\log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(x \right)}} - \frac{6 \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \frac{6 \log{\left(x \right)}}{x \left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} + \frac{6 \log{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{6}{x^{2} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + \frac{4 \log{\left(x \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{3}} - \frac{6 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{3}}\right) \operatorname{acos}^{\log{\left(x \right)}^{2}}{\left(x \right)}

Simplificar

Gráfico

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Expresiones idénticas

Expresiones con funciones

Derivada de y=(arccosx)^ln^2x

Gráfico:

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Solución