Sr Examen

Derivada de x^(ln(arcsin(x)))

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
 log(asin(x))
x            
$$x^{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}$$
x^log(asin(x))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
 log(asin(x)) /log(asin(x))          log(x)      \
x            *|------------ + -------------------|
              |     x            ________        |
              |                 /      2         |
              \               \/  1 - x  *asin(x)/
$$x^{\log{\left(\operatorname{asin}{\left(x \right)} \right)}} \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x}\right)$$
Segunda derivada [src]
              /                                    2                                                                                  \
 log(asin(x)) |/log(asin(x))          log(x)      \    log(asin(x))         log(x)                   2                   x*log(x)     |
x            *||------------ + -------------------|  - ------------ + ------------------ + --------------------- + -------------------|
              ||     x            ________        |          2        /      2\     2           ________                   3/2        |
              ||                 /      2         |         x         \-1 + x /*asin (x)       /      2            /     2\           |
              \\               \/  1 - x  *asin(x)/                                        x*\/  1 - x  *asin(x)   \1 - x /   *asin(x)/
$$x^{\log{\left(\operatorname{asin}{\left(x \right)} \right)}} \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x}\right)^{2} + \frac{\log{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{2}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x^{2}}\right)$$
Tercera derivada [src]
              /                                    3                                                                                                                                                                                                                                                                                                 2           \
 log(asin(x)) |/log(asin(x))          log(x)      \    2*log(asin(x))            3              /log(asin(x))          log(x)      \ /  log(asin(x))         log(x)                   2                   x*log(x)     \          log(x)                   3                    2*log(x)                  3                  3*x*log(x)           3*x *log(x)    |
x            *||------------ + -------------------|  + -------------- + ------------------- + 3*|------------ + -------------------|*|- ------------ + ------------------ + --------------------- + -------------------| + ------------------- - ---------------------- + -------------------- + -------------------- - ------------------- + -------------------|
              ||     x            ________        |           3                 3/2             |     x            ________        | |        2        /      2\     2           ________                   3/2        |           3/2                 ________                   3/2              /      2\     2               2                    5/2        |
              ||                 /      2         |          x          /     2\                |                 /      2         | |       x         \-1 + x /*asin (x)       /      2            /     2\           |   /     2\               2   /      2            /     2\        3      x*\-1 + x /*asin (x)   /      2\      2      /     2\           |
              \\               \/  1 - x  *asin(x)/                     \1 - x /   *asin(x)     \               \/  1 - x  *asin(x)/ \                                      x*\/  1 - x  *asin(x)   \1 - x /   *asin(x)/   \1 - x /   *asin(x)   x *\/  1 - x  *asin(x)   \1 - x /   *asin (x)                          \-1 + x / *asin (x)   \1 - x /   *asin(x)/
$$x^{\log{\left(\operatorname{asin}{\left(x \right)} \right)}} \left(\frac{3 x^{2} \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(x \right)}} - \frac{3 x \log{\left(x \right)}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x}\right)^{3} + 3 \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x}\right) \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{\log{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{2}{x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x^{2}}\right) + \frac{\log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{2 \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(x \right)}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{3}{x \left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} - \frac{3}{x^{2} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{2 \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{x^{3}}\right)$$
Gráfico
Derivada de x^(ln(arcsin(x)))