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Derivada de la función/ sin2x/ y=e^x/ e^x^3/ arcsin/ y=e^x^3arcsin2x

Derivada de y=e^x^3arcsin2x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
 / 3\          
 \x /          
E    *asin(2*x)
ex3asin⁡(2x)e^{x^{3}} \operatorname{asin}{\left(2 x \right)} 
E^(x^3)*asin(2*x)
Primera derivada [src] 
      / 3\                          
      \x /                      / 3\
   2*e             2            \x /
------------- + 3*x *asin(2*x)*e    
   __________                       
  /        2                        
\/  1 - 4*x
3x2ex3asin⁡(2x)+2ex31−4x23 x^{2} e^{x^{3}} \operatorname{asin}{\left(2 x \right)} + \frac{2 e^{x^{3}}}{\sqrt{1 - 4 x^{2}}}
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Segunda derivada [src] 
                                                            / 3\
  /      8           /       3\                  12*x    \  \x /
x*|------------- + 3*\2 + 3*x /*asin(2*x) + -------------|*e    
  |          3/2                               __________|      
  |/       2\                                 /        2 |      
  \\1 - 4*x /                               \/  1 - 4*x  /
x(12x1−4x2+3(3x3+2)asin⁡(2x)+8(1−4x2)32)ex3x \left(\frac{12 x}{\sqrt{1 - 4 x^{2}}} + 3 \left(3 x^{3} + 2\right) \operatorname{asin}{\left(2 x \right)} + \frac{8}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right) e^{x^{3}}
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Tercera derivada [src] 
/    /           2  \                                                                   \      
|    |       12*x   |                                                                   |      
|  8*|-1 + ---------|                                                                   |      
|    |             2|                                            3            /       3\|  / 3\
|    \     -1 + 4*x /     /       6       3\                 72*x        18*x*\2 + 3*x /|  \x /
|- ------------------ + 3*\2 + 9*x  + 18*x /*asin(2*x) + ------------- + ---------------|*e    
|              3/2                                                 3/2       __________ |      
|    /       2\                                          /       2\         /        2  |      
\    \1 - 4*x /                                          \1 - 4*x /       \/  1 - 4*x   /
(72x3(1−4x2)32+18x(3x3+2)1−4x2+3(9x6+18x3+2)asin⁡(2x)−8(12x24x2−1−1)(1−4x2)32)ex3\left(\frac{72 x^{3}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{18 x \left(3 x^{3} + 2\right)}{\sqrt{1 - 4 x^{2}}} + 3 \left(9 x^{6} + 18 x^{3} + 2\right) \operatorname{asin}{\left(2 x \right)} - \frac{8 \left(\frac{12 x^{2}}{4 x^{2} - 1} - 1\right)}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right) e^{x^{3}}
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