Derivada de Кореньизx^asinx

Solución

Ha introducido [src]

 / -asin(x)\
 \2        /
x

$$x^{\left(\frac{1}{2}\right)^{\operatorname{asin}{\left(x \right)}}}$$

x^((1/2)^asin(x))

Solución detallada

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

Perola derivada

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

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

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Derivada de Кореньизx^asinx

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