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Derivada de la función/ (x^4)/ sin(x)/ arcsin/ y=(arcsin(x))^(x^4)

Derivada de y=(arcsin(x))^(x^4)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
         / 4\
         \x /
(asin(x))
asin⁡x4(x)\operatorname{asin}^{x^{4}}{\left(x \right)} 
asin(x)^(x^4)
Solución detallada

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

    Perola derivada

    (log⁡(x4)+1)∣x∣4x4\left(\log{\left(x^{4} \right)} + 1\right) \left|{x}\right|^{4 x^{4}}

Respuesta:

(log⁡(x4)+1)∣x∣4x4\left(\log{\left(x^{4} \right)} + 1\right) \left|{x}\right|^{4 x^{4}}

Primera derivada [src] 
         / 4\ /                              4        \
         \x / |   3                         x         |
(asin(x))    *|4*x *log(asin(x)) + -------------------|
              |                       ________        |
              |                      /      2         |
              \                    \/  1 - x  *asin(x)/
(x41−x2asin⁡(x)+4x3log⁡(asin⁡(x)))asin⁡x4(x)\left(\frac{x^{4}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 4 x^{3} \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) \operatorname{asin}^{x^{4}}{\left(x \right)}
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Segunda derivada [src] 
            / 4\ /                                                           2            2                     3                              \
 2          \x / |                   4 /                          x         \            x                     x                    8*x        |
x *(asin(x))    *|12*log(asin(x)) + x *|4*log(asin(x)) + -------------------|  + ------------------ + ------------------- + -------------------|
                 |                     |                    ________        |    /      2\     2              3/2              ________        |
                 |                     |                   /      2         |    \-1 + x /*asin (x)   /     2\                /      2         |
                 \                     \                 \/  1 - x  *asin(x)/                         \1 - x /   *asin(x)   \/  1 - x  *asin(x)/
x2(x4(x1−x2asin⁡(x)+4log⁡(asin⁡(x)))2+x3(1−x2)32asin⁡(x)+x2(x2−1)asin⁡2(x)+8x1−x2asin⁡(x)+12log⁡(asin⁡(x)))asin⁡x4(x)x^{2} \left(x^{4} \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 4 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right)^{2} + \frac{x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{x^{2}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{8 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 12 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) \operatorname{asin}^{x^{4}}{\left(x \right)}
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Tercera derivada [src] 
           / 4\ /                                                           3              4                     3                                                       /                           2                     3                              \              5                    2                     3                             \
           \x / |                   8 /                          x         \            3*x                   2*x               4 /                          x         \ |                          x                     x                    8*x        |           3*x                 12*x                  13*x                   36*x       |
x*(asin(x))    *|24*log(asin(x)) + x *|4*log(asin(x)) + -------------------|  - ------------------- + -------------------- + 3*x *|4*log(asin(x)) + -------------------|*|12*log(asin(x)) + ------------------ + ------------------- + -------------------| + ------------------- + ------------------ + ------------------- + -------------------|
                |                     |                    ________        |             2                    3/2                 |                    ________        | |                  /      2\     2              3/2              ________        |           5/2           /      2\     2              3/2              ________        |
                |                     |                   /      2         |    /      2\      2      /     2\        3           |                   /      2         | |                  \-1 + x /*asin (x)   /     2\                /      2         |   /     2\              \-1 + x /*asin (x)   /     2\                /      2         |
                \                     \                 \/  1 - x  *asin(x)/    \-1 + x / *asin (x)   \1 - x /   *asin (x)        \                 \/  1 - x  *asin(x)/ \                                       \1 - x /   *asin(x)   \/  1 - x  *asin(x)/   \1 - x /   *asin(x)                        \1 - x /   *asin(x)   \/  1 - x  *asin(x)/
x(x8(x1−x2asin⁡(x)+4log⁡(asin⁡(x)))3+3x5(1−x2)52asin⁡(x)+3x4(x1−x2asin⁡(x)+4log⁡(asin⁡(x)))(x3(1−x2)32asin⁡(x)+x2(x2−1)asin⁡2(x)+8x1−x2asin⁡(x)+12log⁡(asin⁡(x)))−3x4(x2−1)2asin⁡2(x)+13x3(1−x2)32asin⁡(x)+2x3(1−x2)32asin⁡3(x)+12x2(x2−1)asin⁡2(x)+36x1−x2asin⁡(x)+24log⁡(asin⁡(x)))asin⁡x4(x)x \left(x^{8} \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 4 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right)^{3} + \frac{3 x^{5}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(x \right)}} + 3 x^{4} \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 4 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) \left(\frac{x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{x^{2}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{8 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 12 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) - \frac{3 x^{4}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(x \right)}} + \frac{13 x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{2 x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(x \right)}} + \frac{12 x^{2}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{36 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 24 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) \operatorname{asin}^{x^{4}}{\left(x \right)}
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