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e^x^2*asin(3*x)

Derivada de e^x^2*asin(3*x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
 / 2\          
 \x /          
E    *asin(3*x)
$$e^{x^{2}} \operatorname{asin}{\left(3 x \right)}$$
E^(x^2)*asin(3*x)
Gráfica
Primera derivada [src]
      / 2\                         
      \x /                     / 2\
   3*e                         \x /
------------- + 2*x*asin(3*x)*e    
   __________                      
  /        2                       
\/  1 - 9*x                        
$$2 x e^{x^{2}} \operatorname{asin}{\left(3 x \right)} + \frac{3 e^{x^{2}}}{\sqrt{1 - 9 x^{2}}}$$
Segunda derivada [src]
                                                          / 2\
/  /       2\                  12*x            27*x    \  \x /
|2*\1 + 2*x /*asin(3*x) + ------------- + -------------|*e    
|                            __________             3/2|      
|                           /        2    /       2\   |      
\                         \/  1 - 9*x     \1 - 9*x /   /      
$$\left(\frac{12 x}{\sqrt{1 - 9 x^{2}}} + \frac{27 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + 2 \left(2 x^{2} + 1\right) \operatorname{asin}{\left(3 x \right)}\right) e^{x^{2}}$$
Tercera derivada [src]
/     /           2  \                                                           \      
|     |       27*x   |                                                           |      
|  27*|-1 + ---------|                                                           |      
|     |             2|      /       2\            2                              |  / 2\
|     \     -1 + 9*x /   18*\1 + 2*x /       162*x           /       2\          |  \x /
|- ------------------- + ------------- + ------------- + 4*x*\3 + 2*x /*asin(3*x)|*e    
|               3/2         __________             3/2                           |      
|     /       2\           /        2    /       2\                              |      
\     \1 - 9*x /         \/  1 - 9*x     \1 - 9*x /                              /      
$$\left(\frac{162 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + 4 x \left(2 x^{2} + 3\right) \operatorname{asin}{\left(3 x \right)} + \frac{18 \left(2 x^{2} + 1\right)}{\sqrt{1 - 9 x^{2}}} - \frac{27 \left(\frac{27 x^{2}}{9 x^{2} - 1} - 1\right)}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) e^{x^{2}}$$
Gráfico
Derivada de e^x^2*asin(3*x)