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y=e^(arcsin(5x)/x)
Derivada de la función/ arcsin/ sin(5x)/ y=e^(arcsin(5x)/x)

Derivada de y=e^(arcsin(5x)/x)

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

Ha introducido [src] 
 asin(5*x)
 ---------
     x    
E
easin⁡(5x)xe^{\frac{\operatorname{asin}{\left(5 x \right)}}{x}} 
E^(asin(5*x)/x)
Gráfica
02468-8-6-4-2-1010-25002500
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Primera derivada [src] 
                                  asin(5*x)
                                  ---------
/  asin(5*x)          5        \      x    
|- --------- + ----------------|*e         
|       2           ___________|           
|      x           /         2 |           
\              x*\/  1 - 25*x  /
(5x1−25x2−asin⁡(5x)x2)easin⁡(5x)x\left(\frac{5}{x \sqrt{1 - 25 x^{2}}} - \frac{\operatorname{asin}{\left(5 x \right)}}{x^{2}}\right) e^{\frac{\operatorname{asin}{\left(5 x \right)}}{x}}
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Segunda derivada [src] 
/                                             2                                  \           
|                 /      5          asin(5*x)\                                   |           
|                 |-------------- - ---------|                                   |           
|                 |   ___________       x    |                                   |  asin(5*x)
|                 |  /         2             |                                   |  ---------
|     125         \\/  1 - 25*x              /            10          2*asin(5*x)|      x    
|-------------- + ----------------------------- - ----------------- + -----------|*e         
|           3/2                  2                      ___________         3    |           
|/        2\                    x                  2   /         2         x     |           
\\1 - 25*x /                                      x *\/  1 - 25*x                /
(125(1−25x2)32+(51−25x2−asin⁡(5x)x)2x2−10x21−25x2+2asin⁡(5x)x3)easin⁡(5x)x\left(\frac{125}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{\left(\frac{5}{\sqrt{1 - 25 x^{2}}} - \frac{\operatorname{asin}{\left(5 x \right)}}{x}\right)^{2}}{x^{2}} - \frac{10}{x^{2} \sqrt{1 - 25 x^{2}}} + \frac{2 \operatorname{asin}{\left(5 x \right)}}{x^{3}}\right) e^{\frac{\operatorname{asin}{\left(5 x \right)}}{x}}
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Tercera derivada [src] 
/                            3                                                                                                                                                          \           
|/      5          asin(5*x)\                                                                            /      5          asin(5*x)\ /     125                 10          2*asin(5*x)\|           
||-------------- - ---------|                                                                          3*|-------------- - ---------|*|-------------- - ----------------- + -----------||           
||   ___________       x    |                                                                            |   ___________       x    | |           3/2         ___________         3    ||  asin(5*x)
||  /         2             |                                                                            |  /         2             | |/        2\       2   /         2         x     ||  ---------
|\\/  1 - 25*x              /          250          6*asin(5*x)           30              9375*x         \\/  1 - 25*x              / \\1 - 25*x /      x *\/  1 - 25*x                /|      x    
|----------------------------- - ---------------- - ----------- + ----------------- + -------------- + ---------------------------------------------------------------------------------|*e         
|               3                             3/2         4             ___________              5/2                                           x                                        |           
|              x                   /        2\           x         3   /         2    /        2\                                                                                       |           
\                                x*\1 - 25*x /                    x *\/  1 - 25*x     \1 - 25*x /                                                                                       /
(9375x(1−25x2)52+3(51−25x2−asin⁡(5x)x)(125(1−25x2)32−10x21−25x2+2asin⁡(5x)x3)x−250x(1−25x2)32+(51−25x2−asin⁡(5x)x)3x3+30x31−25x2−6asin⁡(5x)x4)easin⁡(5x)x\left(\frac{9375 x}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{3 \left(\frac{5}{\sqrt{1 - 25 x^{2}}} - \frac{\operatorname{asin}{\left(5 x \right)}}{x}\right) \left(\frac{125}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \frac{10}{x^{2} \sqrt{1 - 25 x^{2}}} + \frac{2 \operatorname{asin}{\left(5 x \right)}}{x^{3}}\right)}{x} - \frac{250}{x \left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{\left(\frac{5}{\sqrt{1 - 25 x^{2}}} - \frac{\operatorname{asin}{\left(5 x \right)}}{x}\right)^{3}}{x^{3}} + \frac{30}{x^{3} \sqrt{1 - 25 x^{2}}} - \frac{6 \operatorname{asin}{\left(5 x \right)}}{x^{4}}\right) e^{\frac{\operatorname{asin}{\left(5 x \right)}}{x}}
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Gráfico
Derivada de y=e^(arcsin(5x)/x)
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