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y=5^(-x)^2*asin(3*x)^3
Derivada de la función/ sin(3*x)/ y=5^(-x)^2*asin(3*x)^3

Derivada de y=5^(-x)^2*asin(3*x)^3

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

Ha introducido [src] 
 /    2\           
 \(-x) /     3     
5       *asin (3*x)
5(−x)2asin⁡3(3x)5^{\left(- x\right)^{2}} \operatorname{asin}^{3}{\left(3 x \right)} 
5^((-x)^2)*asin(3*x)^3
Gráfica
02468-8-6-4-2-1010-5050
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Primera derivada [src] 
   /    2\                                            
   \(-x) /     2             /    2\                  
9*5       *asin (3*x)        \(-x) /     3            
--------------------- + 2*x*5       *asin (3*x)*log(5)
       __________                                     
      /        2                                      
    \/  1 - 9*x
2⋅5(−x)2xlog⁡(5)asin⁡3(3x)+9⋅5(−x)2asin⁡2(3x)1−9x22 \cdot 5^{\left(- x\right)^{2}} x \log{\left(5 \right)} \operatorname{asin}^{3}{\left(3 x \right)} + \frac{9 \cdot 5^{\left(- x\right)^{2}} \operatorname{asin}^{2}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}
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Segunda derivada [src] 
 / 2\                                                                                                         
 \x / /      54            2      /       2       \          81*x*asin(3*x)   36*x*asin(3*x)*log(5)\          
5    *|- --------- + 2*asin (3*x)*\1 + 2*x *log(5)/*log(5) + -------------- + ---------------------|*asin(3*x)
      |          2                                                     3/2           __________    |          
      |  -1 + 9*x                                            /       2\             /        2     |          
      \                                                      \1 - 9*x /           \/  1 - 9*x      /
5x2(36xlog⁡(5)asin⁡(3x)1−9x2+81xasin⁡(3x)(1−9x2)32+2(2x2log⁡(5)+1)log⁡(5)asin⁡2(3x)−549x2−1)asin⁡(3x)5^{x^{2}} \left(\frac{36 x \log{\left(5 \right)} \operatorname{asin}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}} + \frac{81 x \operatorname{asin}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + 2 \left(2 x^{2} \log{\left(5 \right)} + 1\right) \log{\left(5 \right)} \operatorname{asin}^{2}{\left(3 x \right)} - \frac{54}{9 x^{2} - 1}\right) \operatorname{asin}{\left(3 x \right)}
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Tercera derivada [src] 
 / 2\ /                       2                                 2     2                                                          2      /       2       \                                                              \
 \x / |     162        81*asin (3*x)   1458*x*asin(3*x)   2187*x *asin (3*x)           3         2    /       2       \   54*asin (3*x)*\1 + 2*x *log(5)/*log(5)         /      2       3*x*asin(3*x)\                 |
5    *|------------- + ------------- + ---------------- + ------------------ + 4*x*asin (3*x)*log (5)*\3 + 2*x *log(5)/ + -------------------------------------- + 162*x*|- --------- + -------------|*asin(3*x)*log(5)|
      |          3/2             3/2                2                 5/2                                                                __________                      |          2             3/2|                 |
      |/       2\      /       2\        /        2\        /       2\                                                                  /        2                       |  -1 + 9*x    /       2\   |                 |
      \\1 - 9*x /      \1 - 9*x /        \-1 + 9*x /        \1 - 9*x /                                                                \/  1 - 9*x                        \              \1 - 9*x /   /                 /
5x2(2187x2asin⁡2(3x)(1−9x2)52+4x(2x2log⁡(5)+3)log⁡(5)2asin⁡3(3x)+162x(3xasin⁡(3x)(1−9x2)32−29x2−1)log⁡(5)asin⁡(3x)+1458xasin⁡(3x)(9x2−1)2+54(2x2log⁡(5)+1)log⁡(5)asin⁡2(3x)1−9x2+81asin⁡2(3x)(1−9x2)32+162(1−9x2)32)5^{x^{2}} \left(\frac{2187 x^{2} \operatorname{asin}^{2}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + 4 x \left(2 x^{2} \log{\left(5 \right)} + 3\right) \log{\left(5 \right)}^{2} \operatorname{asin}^{3}{\left(3 x \right)} + 162 x \left(\frac{3 x \operatorname{asin}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{9 x^{2} - 1}\right) \log{\left(5 \right)} \operatorname{asin}{\left(3 x \right)} + \frac{1458 x \operatorname{asin}{\left(3 x \right)}}{\left(9 x^{2} - 1\right)^{2}} + \frac{54 \left(2 x^{2} \log{\left(5 \right)} + 1\right) \log{\left(5 \right)} \operatorname{asin}^{2}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}} + \frac{81 \operatorname{asin}^{2}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{162}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right)
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Gráfico
Derivada de y=5^(-x)^2*asin(3*x)^3
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