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е^(x/arcsinx)
Derivada de la función/ arcsin/ е^(x/arcsinx)

Derivada de е^(x/arcsinx)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    x   
 -------
 asin(x)
E
exasin⁡(x)e^{\frac{x}{\operatorname{asin}{\left(x \right)}}} 
E^(x/asin(x))
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                     x   
                                  -------
/   1               x          \  asin(x)
|------- - --------------------|*e       
|asin(x)      ________         |         
|            /      2      2   |         
\          \/  1 - x  *asin (x)/
(−x1−x2asin⁡2(x)+1asin⁡(x))exasin⁡(x)\left(- \frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}} + \frac{1}{\operatorname{asin}{\left(x \right)}}\right) e^{\frac{x}{\operatorname{asin}{\left(x \right)}}}
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Segunda derivada [src] 
                                                                                  x   
/                          2                       2                        \  -------
|/              x         \         2             x               2*x       |  asin(x)
||-1 + -------------------|  - ----------- - ----------- - -----------------|*e       
||        ________        |       ________           3/2   /      2\        |         
||       /      2         |      /      2    /     2\      \-1 + x /*asin(x)|         
\\     \/  1 - x  *asin(x)/    \/  1 - x     \1 - x /                       /         
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                                           2                                          
                                       asin (x)
(−x2(1−x2)32−2x(x2−1)asin⁡(x)+(x1−x2asin⁡(x)−1)2−21−x2)exasin⁡(x)asin⁡2(x)\frac{\left(- \frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} + \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - 1\right)^{2} - \frac{2}{\sqrt{1 - x^{2}}}\right) e^{\frac{x}{\operatorname{asin}{\left(x \right)}}}}{\operatorname{asin}^{2}{\left(x \right)}}
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Tercera derivada [src] 
/                            3                                                                                                       /                    2                        \                     \         
|  /              x         \                                                                             /              x         \ |     2             x               2*x       |                     |         
|  |-1 + -------------------|                                                                           3*|-1 + -------------------|*|----------- + ----------- + -----------------|                     |         
|  |        ________        |                                                                             |        ________        | |   ________           3/2   /      2\        |                     |     x   
|  |       /      2         |                                             3                               |       /      2         | |  /      2    /     2\      \-1 + x /*asin(x)|             2       |  -------
|  \     \/  1 - x  *asin(x)/            6               4*x           3*x               6*x              \     \/  1 - x  *asin(x)/ \\/  1 - x     \1 - x /                       /          6*x        |  asin(x)
|- --------------------------- - ----------------- - ----------- - ----------- - -------------------- + ---------------------------------------------------------------------------- + ------------------|*e       
|            asin(x)             /      2\                   3/2           5/2           3/2                                              asin(x)                                               2        |         
|                                \-1 + x /*asin(x)   /     2\      /     2\      /     2\        2                                                                                     /      2\         |         
\                                                    \1 - x /      \1 - x /      \1 - x /   *asin (x)                                                                                  \-1 + x / *asin(x)/         
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                          2                                                                                                        
                                                                                                      asin (x)
(−3x3(1−x2)52+6x2(x2−1)2asin⁡(x)−4x(1−x2)32−6x(1−x2)32asin⁡2(x)−(x1−x2asin⁡(x)−1)3asin⁡(x)+3(x1−x2asin⁡(x)−1)(x2(1−x2)32+2x(x2−1)asin⁡(x)+21−x2)asin⁡(x)−6(x2−1)asin⁡(x))exasin⁡(x)asin⁡2(x)\frac{\left(- \frac{3 x^{3}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} - \frac{4 x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}} - \frac{\left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - 1\right)^{3}}{\operatorname{asin}{\left(x \right)}} + \frac{3 \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - 1\right) \left(\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} + \frac{2}{\sqrt{1 - x^{2}}}\right)}{\operatorname{asin}{\left(x \right)}} - \frac{6}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right) e^{\frac{x}{\operatorname{asin}{\left(x \right)}}}}{\operatorname{asin}^{2}{\left(x \right)}}
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Gráfico
Derivada de е^(x/arcsinx)
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