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(sqrt(x))^arcsin(x)
Derivada de la función/ sin(x)/ arcsin/ sqrt(x)/ (sqrt(x))^arcsin(x)

Derivada de (sqrt(x))^arcsin(x)

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

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

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

    Perola derivada

    (log⁡(asin⁡(x))+1)asin⁡asin⁡(x)(x)\left(\log{\left(\operatorname{asin}{\left(x \right)} \right)} + 1\right) \operatorname{asin}^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}

Respuesta:

(log⁡(asin⁡(x))+1)asin⁡asin⁡(x)(x)\left(\log{\left(\operatorname{asin}{\left(x \right)} \right)} + 1\right) \operatorname{asin}^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}

Gráfica
02468-8-6-4-2-10102-2
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Primera derivada [src] 
 asin(x)                        
 ------- /    /  ___\          \
    2    | log\\/ x /   asin(x)|
x       *|----------- + -------|
         |   ________     2*x  |
         |  /      2           |
         \\/  1 - x            /
xasin⁡(x)2(log⁡(x)1−x2+asin⁡(x)2x)x^{\frac{\operatorname{asin}{\left(x \right)}}{2}} \left(\frac{\log{\left(\sqrt{x} \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{2 x}\right)
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Segunda derivada [src] 
         /                                                  /               /  ___\\               \
         |                          /asin(x)      log(x)  \ |asin(x)   2*log\\/ x /|               |
         |                          |------- + -----------|*|------- + ------------|               |
 asin(x) |                          |   x         ________| |   x         ________ |               |
 ------- |                          |            /      2 | |            /      2  |        /  ___\|
    2    |      1         asin(x)   \          \/  1 - x  / \          \/  1 - x   /   x*log\\/ x /|
x       *|------------- - ------- + ------------------------------------------------ + ------------|
         |     ________        2                           4                                   3/2 |
         |    /      2      2*x                                                        /     2\    |
         \x*\/  1 - x                                                                  \1 - x /    /
xasin⁡(x)2(xlog⁡(x)(1−x2)32+(2log⁡(x)1−x2+asin⁡(x)x)(log⁡(x)1−x2+asin⁡(x)x)4+1x1−x2−asin⁡(x)2x2)x^{\frac{\operatorname{asin}{\left(x \right)}}{2}} \left(\frac{x \log{\left(\sqrt{x} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\left(\frac{2 \log{\left(\sqrt{x} \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right) \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right)}{4} + \frac{1}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}{\left(x \right)}}{2 x^{2}}\right)
Simplificar
Tercera derivada [src] 
         /                                                                /                                   /  ___\\                      /               /  ___\\                                                                    2 /               /  ___\\                  \
         |                                        /asin(x)      log(x)  \ |  asin(x)         2         2*x*log\\/ x /|                      |asin(x)   2*log\\/ x /| /  asin(x)         2           x*log(x) \   /asin(x)      log(x)  \  |asin(x)   2*log\\/ x /|                  |
         |                                        |------- + -----------|*|- ------- + ------------- + --------------|                      |------- + ------------|*|- ------- + ------------- + -----------|   |------- + -----------| *|------- + ------------|                  |
 asin(x) |                                        |   x         ________| |      2          ________            3/2  |                      |   x         ________ | |      2          ________           3/2|   |   x         ________|  |   x         ________ |                  |
 ------- |                              /  ___\   |            /      2 | |     x          /      2     /     2\     |                      |            /      2  | |     x          /      2    /     2\   |   |            /      2 |  |            /      2  |      2    /  ___\|
    2    |      3         asin(x)    log\\/ x /   \          \/  1 - x  / \            x*\/  1 - x      \1 - x /     /          3           \          \/  1 - x   / \            x*\/  1 - x     \1 - x /   /   \          \/  1 - x  /  \          \/  1 - x   /   3*x *log\\/ x /|
x       *|------------- + ------- + ----------- + -------------------------------------------------------------------- - ---------------- + ------------------------------------------------------------------ + ------------------------------------------------- + ---------------|
         |          3/2       3             3/2                                    2                                             ________                                   4                                                            8                                     5/2  |
         |  /     2\         x      /     2\                                                                                2   /      2                                                                                                                               /     2\     |
         \2*\1 - x /                \1 - x /                                                                             2*x *\/  1 - x                                                                                                                                \1 - x /     /
xasin⁡(x)2(3x2log⁡(x)(1−x2)52+(2log⁡(x)1−x2+asin⁡(x)x)(log⁡(x)1−x2+asin⁡(x)x)28+(2log⁡(x)1−x2+asin⁡(x)x)(xlog⁡(x)(1−x2)32+2x1−x2−asin⁡(x)x2)4+(log⁡(x)1−x2+asin⁡(x)x)(2xlog⁡(x)(1−x2)32+2x1−x2−asin⁡(x)x2)2+log⁡(x)(1−x2)32+32(1−x2)32−32x21−x2+asin⁡(x)x3)x^{\frac{\operatorname{asin}{\left(x \right)}}{2}} \left(\frac{3 x^{2} \log{\left(\sqrt{x} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{\left(\frac{2 \log{\left(\sqrt{x} \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right) \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right)^{2}}{8} + \frac{\left(\frac{2 \log{\left(\sqrt{x} \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right) \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}{\left(x \right)}}{x^{2}}\right)}{4} + \frac{\left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x}\right) \left(\frac{2 x \log{\left(\sqrt{x} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}{\left(x \right)}}{x^{2}}\right)}{2} + \frac{\log{\left(\sqrt{x} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{2 \left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{2 x^{2} \sqrt{1 - x^{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{x^{3}}\right)
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Gráfico
Derivada de (sqrt(x))^arcsin(x)
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