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(asin(x))^√(1-x)
(asin(x))sqrt(1-x)
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Expresiones con funciones
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Raíz cuadrada sqrt
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sqrt(x)-1/(sqrt(x)*2-x-1)
sqrt(x)*(x^4+2)

Derivada de la función/ sin(x)/ (1-x)/ (asin(x))^sqrt(1-x)

Derivada de (asin(x))^sqrt(1-x)

Solución

Ha introducido [src]

           _______
         \/ 1 - x 
(asin(x))

\operatorname{asin}^{\sqrt{1 - x}}{\left(x \right)}

asin(x)^(sqrt(1 - x))

Solución detallada

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

Perola derivada

$\left(1 - x\right)^{\frac{\sqrt{1 - x}}{2}} \left(\log{\left(\sqrt{1 - x} \right)} + 1\right)$
Simplificamos:

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

                   /                                      3                                                                                                                                                                                                                                                                                                                                                       \
                   |/                         _______    \                       /                         _______    \ /                                                        _______                _______   \                                                                                                                                                                                               |
                   ||  log(asin(x))       2*\/ 1 - x     |                       |  log(asin(x))       2*\/ 1 - x     | |  log(asin(x))                 4                    4*\/ 1 - x           4*x*\/ 1 - x    |                                                                                                                                                                                               |
                   ||- ------------ + -------------------|                     3*|- ------------ + -------------------|*|- ------------ - ----------------------------- + ------------------ + -------------------|                                                                                                                                                                                               |
                   ||     _______        ________        |                       |     _______        ________        | |          3/2                 ________           /      2\     2              3/2        |                                                                                                                                                                                               |
           _______ ||   \/ 1 - x        /      2         |                       |   \/ 1 - x        /      2         | |   (1 - x)         _______   /      2            \-1 + x /*asin (x)   /     2\           |          _______                _______                                                                                     _______            2   _______                                    |
         \/ 1 - x  |\                 \/  1 - x  *asin(x)/    3*log(asin(x))     \                 \/  1 - x  *asin(x)/ \                 \/ 1 - x *\/  1 - x  *asin(x)                        \1 - x /   *asin(x)/        \/ 1 - x             2*\/ 1 - x                       3                                 3                      3*x*\/ 1 - x          3*x *\/ 1 - x                    3*x              |
(asin(x))         *|--------------------------------------- - -------------- + ------------------------------------------------------------------------------------------------------------------------------------ + ------------------- + -------------------- - ------------------------------ - -------------------------------- - ------------------- + ------------------- - -------------------------------|
                   |                   8                                5/2                                                                     8                                                                             3/2                   3/2                _______ /      2\     2                      ________                    2                    5/2                               3/2        |
                   |                                           8*(1 - x)                                                                                                                                              /     2\              /     2\        3      2*\/ 1 - x *\-1 + x /*asin (x)            3/2   /      2            /      2\      2      /     2\                  _______ /     2\           |
                   \                                                                                                                                                                                                  \1 - x /   *asin(x)   \1 - x /   *asin (x)                                    4*(1 - x)   *\/  1 - x  *asin(x)   \-1 + x / *asin (x)   \1 - x /   *asin(x)   2*\/ 1 - x *\1 - x /   *asin(x)/

\left(\frac{3 x^{2} \sqrt{1 - x}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(x \right)}} - \frac{3 x \sqrt{1 - x}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(x \right)}} - \frac{3 x}{2 \sqrt{1 - x} \left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{\sqrt{1 - x}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{2 \sqrt{1 - x}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(x \right)}} + \frac{\left(\frac{2 \sqrt{1 - x}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x}}\right)^{3}}{8} + \frac{3 \left(\frac{2 \sqrt{1 - x}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\sqrt{1 - x}}\right) \left(\frac{4 x \sqrt{1 - x}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{4 \sqrt{1 - x}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} - \frac{4}{\sqrt{1 - x} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x\right)^{\frac{3}{2}}}\right)}{8} - \frac{3}{2 \sqrt{1 - x} \left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} - \frac{3}{4 \left(1 - x\right)^{\frac{3}{2}} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{3 \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{8 \left(1 - x\right)^{\frac{5}{2}}}\right) \operatorname{asin}^{\sqrt{1 - x}}{\left(x \right)}

Simplificar

Gráfico

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Derivada de (asin(x))^sqrt(1-x)

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Solución