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y'=e^(-x)*asin(5*x)^2
Derivada de la función/ e^(-x)/ sin(5*x)/ y'=e^(-x)*asin(5*x)^2

Derivada de y'=e^(-x)*asin(5*x)^2

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
 -x     2     
E  *asin (5*x)
e−xasin⁡2(5x)e^{- x} \operatorname{asin}^{2}{\left(5 x \right)} 
E^(-x)*asin(5*x)^2
Gráfica
02468-8-6-4-2-1010-1010
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Primera derivada [src] 
                                 -x
      2       -x   10*asin(5*x)*e  
- asin (5*x)*e   + ----------------
                       ___________ 
                      /         2  
                    \/  1 - 25*x
−e−xasin⁡2(5x)+10e−xasin⁡(5x)1−25x2- e^{- x} \operatorname{asin}^{2}{\left(5 x \right)} + \frac{10 e^{- x} \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}
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Segunda derivada [src] 
/    2            50        20*asin(5*x)    250*x*asin(5*x)\  -x
|asin (5*x) - ---------- - -------------- + ---------------|*e  
|                      2      ___________               3/2|    
|             -1 + 25*x      /         2     /        2\   |    
\                          \/  1 - 25*x      \1 - 25*x /   /
(250xasin⁡(5x)(1−25x2)32+asin⁡2(5x)−5025x2−1−20asin⁡(5x)1−25x2)e−x\left(\frac{250 x \operatorname{asin}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \operatorname{asin}^{2}{\left(5 x \right)} - \frac{50}{25 x^{2} - 1} - \frac{20 \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}\right) e^{- x}
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3-я производная [src] 
/                                                                                                       2          \    
|      2           150        30*asin(5*x)    250*asin(5*x)        3750*x      750*x*asin(5*x)   18750*x *asin(5*x)|  -x
|- asin (5*x) + ---------- + -------------- + -------------- + ------------- - --------------- + ------------------|*e  
|                        2      ___________              3/2               2               3/2                5/2  |    
|               -1 + 25*x      /         2    /        2\      /         2\     /        2\        /        2\     |    
\                            \/  1 - 25*x     \1 - 25*x /      \-1 + 25*x /     \1 - 25*x /        \1 - 25*x /     /
(18750x2asin⁡(5x)(1−25x2)52+3750x(25x2−1)2−750xasin⁡(5x)(1−25x2)32−asin⁡2(5x)+15025x2−1+30asin⁡(5x)1−25x2+250asin⁡(5x)(1−25x2)32)e−x\left(\frac{18750 x^{2} \operatorname{asin}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{3750 x}{\left(25 x^{2} - 1\right)^{2}} - \frac{750 x \operatorname{asin}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \operatorname{asin}^{2}{\left(5 x \right)} + \frac{150}{25 x^{2} - 1} + \frac{30 \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} + \frac{250 \operatorname{asin}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}\right) e^{- x}
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Tercera derivada [src] 
/                                                                                                       2          \    
|      2           150        30*asin(5*x)    250*asin(5*x)        3750*x      750*x*asin(5*x)   18750*x *asin(5*x)|  -x
|- asin (5*x) + ---------- + -------------- + -------------- + ------------- - --------------- + ------------------|*e  
|                        2      ___________              3/2               2               3/2                5/2  |    
|               -1 + 25*x      /         2    /        2\      /         2\     /        2\        /        2\     |    
\                            \/  1 - 25*x     \1 - 25*x /      \-1 + 25*x /     \1 - 25*x /        \1 - 25*x /     /
(18750x2asin⁡(5x)(1−25x2)52+3750x(25x2−1)2−750xasin⁡(5x)(1−25x2)32−asin⁡2(5x)+15025x2−1+30asin⁡(5x)1−25x2+250asin⁡(5x)(1−25x2)32)e−x\left(\frac{18750 x^{2} \operatorname{asin}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{3750 x}{\left(25 x^{2} - 1\right)^{2}} - \frac{750 x \operatorname{asin}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \operatorname{asin}^{2}{\left(5 x \right)} + \frac{150}{25 x^{2} - 1} + \frac{30 \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} + \frac{250 \operatorname{asin}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}\right) e^{- x}
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Gráfico
Derivada de y'=e^(-x)*asin(5*x)^2
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