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y=arcsin^3(1+e^x^2)
Derivada de la función/ e^x^2/ sin^3/ 1+e^x/ arcsin/ y=arcsin^3(1+e^x^2)

Derivada de y=arcsin^3(1+e^x^2)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
     /     / 2\\
    3|     \x /|
asin \1 + E    /
asin⁡3(ex2+1)\operatorname{asin}^{3}{\left(e^{x^{2}} + 1 \right)} 
asin(1 + E^(x^2))^3
Gráfica
02468-8-6-4-2-10100.02-0.02
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         /     / 2\\  / 2\
        2|     \x /|  \x /
6*x*asin \1 + E    /*e    
--------------------------
      __________________  
     /                2   
    /      /     / 2\\    
   /       |     \x /|    
 \/    1 - \1 + E    /
6xex2asin⁡2(ex2+1)1−(ex2+1)2\frac{6 x e^{x^{2}} \operatorname{asin}^{2}{\left(e^{x^{2}} + 1 \right)}}{\sqrt{1 - \left(e^{x^{2}} + 1\right)^{2}}}
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Segunda derivada [src] 
  /        /     / 2\\                 / 2\                 /     / 2\\         /     / 2\\     /     / 2\\  / 2\\                      
  |        |     \x /|              2  \x /           2     |     \x /|       2 |     \x /|     |     \x /|  \x /|     /     / 2\\  / 2\
  |    asin\1 + e    /           4*x *e            2*x *asin\1 + e    /    2*x *\1 + e    /*asin\1 + e    /*e    |     |     \x /|  \x /
6*|----------------------- - ----------------- + ----------------------- + --------------------------------------|*asin\1 + e    /*e    
  |     __________________                   2        __________________                             3/2         |                      
  |    /                2         /     / 2\\        /                2            /               2\            |                      
  |   /      /     / 2\\          |     \x /|       /      /     / 2\\             |    /     / 2\\ |            |                      
  |  /       |     \x /|     -1 + \1 + e    /      /       |     \x /|             |    |     \x /| |            |                      
  \\/    1 - \1 + e    /                         \/    1 - \1 + e    /             \1 - \1 + e    / /            /
6(−4x2ex2(ex2+1)2−1+2x2asin⁡(ex2+1)1−(ex2+1)2+2x2(ex2+1)ex2asin⁡(ex2+1)(1−(ex2+1)2)32+asin⁡(ex2+1)1−(ex2+1)2)ex2asin⁡(ex2+1)6 \left(- \frac{4 x^{2} e^{x^{2}}}{\left(e^{x^{2}} + 1\right)^{2} - 1} + \frac{2 x^{2} \operatorname{asin}{\left(e^{x^{2}} + 1 \right)}}{\sqrt{1 - \left(e^{x^{2}} + 1\right)^{2}}} + \frac{2 x^{2} \left(e^{x^{2}} + 1\right) e^{x^{2}} \operatorname{asin}{\left(e^{x^{2}} + 1 \right)}}{\left(1 - \left(e^{x^{2}} + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{\operatorname{asin}{\left(e^{x^{2}} + 1 \right)}}{\sqrt{1 - \left(e^{x^{2}} + 1\right)^{2}}}\right) e^{x^{2}} \operatorname{asin}{\left(e^{x^{2}} + 1 \right)}
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Tercera derivada [src] 
     /                                                                                                                                                                                                                         2                                                                                                           \      
     |          /     / 2\\           /     / 2\\  / 2\              /     / 2\\                   2                  /     / 2\\  / 2\             /     / 2\\     2          /     / 2\\ /     / 2\\  / 2\        /     / 2\\       /     / 2\\     2             /     / 2\\ /     / 2\\  / 2\         /     / 2\\     /     / 2\\     2|      
     |         2|     \x /|           |     \x /|  \x /       2     2|     \x /|             2  2*x             2     |     \x /|  \x /      2     2|     \x /|  2*x          2|     \x /| |     \x /|  \x /      2 |     \x /|      2|     \x /|  2*x       2     2|     \x /| |     \x /|  \x /       2 |     \x /|     |     \x /|  2*x |  / 2\
     |   3*asin \1 + e    /     6*asin\1 + e    /*e        2*x *asin \1 + e    /          4*x *e            12*x *asin\1 + e    /*e       2*x *asin \1 + e    /*e       3*asin \1 + e    /*\1 + e    /*e       6*x *\1 + e    / *asin \1 + e    /*e       6*x *asin \1 + e    /*\1 + e    /*e       12*x *\1 + e    /*asin\1 + e    /*e    |  \x /
12*x*|----------------------- - ----------------------- + ----------------------- + --------------------- - --------------------------- + --------------------------- + ------------------------------------ + ---------------------------------------- + --------------------------------------- + ---------------------------------------|*e    
     |     __________________                      2           __________________                     3/2                        2                             3/2                               3/2                                      5/2                                        3/2                                         2         |      
     |    /                2            /     / 2\\           /                2    /               2\                /     / 2\\            /               2\                /               2\                       /               2\                         /               2\                         /                2\          |      
     |   /      /     / 2\\             |     \x /|          /      /     / 2\\     |    /     / 2\\ |                |     \x /|            |    /     / 2\\ |                |    /     / 2\\ |                       |    /     / 2\\ |                         |    /     / 2\\ |                         |     /     / 2\\ |          |      
     |  /       |     \x /|        -1 + \1 + e    /         /       |     \x /|     |    |     \x /| |           -1 + \1 + e    /            |    |     \x /| |                |    |     \x /| |                       |    |     \x /| |                         |    |     \x /| |                         |     |     \x /| |          |      
     \\/    1 - \1 + e    /                               \/    1 - \1 + e    /     \1 - \1 + e    / /                                       \1 - \1 + e    / /                \1 - \1 + e    / /                       \1 - \1 + e    / /                         \1 - \1 + e    / /                         \-1 + \1 + e    / /          /
12x(−12x2ex2asin⁡(ex2+1)(ex2+1)2−1+12x2(ex2+1)e2x2asin⁡(ex2+1)((ex2+1)2−1)2+2x2asin⁡2(ex2+1)1−(ex2+1)2+6x2(ex2+1)ex2asin⁡2(ex2+1)(1−(ex2+1)2)32+2x2e2x2asin⁡2(ex2+1)(1−(ex2+1)2)32+4x2e2x2(1−(ex2+1)2)32+6x2(ex2+1)2e2x2asin⁡2(ex2+1)(1−(ex2+1)2)52−6ex2asin⁡(ex2+1)(ex2+1)2−1+3asin⁡2(ex2+1)1−(ex2+1)2+3(ex2+1)ex2asin⁡2(ex2+1)(1−(ex2+1)2)32)ex212 x \left(- \frac{12 x^{2} e^{x^{2}} \operatorname{asin}{\left(e^{x^{2}} + 1 \right)}}{\left(e^{x^{2}} + 1\right)^{2} - 1} + \frac{12 x^{2} \left(e^{x^{2}} + 1\right) e^{2 x^{2}} \operatorname{asin}{\left(e^{x^{2}} + 1 \right)}}{\left(\left(e^{x^{2}} + 1\right)^{2} - 1\right)^{2}} + \frac{2 x^{2} \operatorname{asin}^{2}{\left(e^{x^{2}} + 1 \right)}}{\sqrt{1 - \left(e^{x^{2}} + 1\right)^{2}}} + \frac{6 x^{2} \left(e^{x^{2}} + 1\right) e^{x^{2}} \operatorname{asin}^{2}{\left(e^{x^{2}} + 1 \right)}}{\left(1 - \left(e^{x^{2}} + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{2 x^{2} e^{2 x^{2}} \operatorname{asin}^{2}{\left(e^{x^{2}} + 1 \right)}}{\left(1 - \left(e^{x^{2}} + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{4 x^{2} e^{2 x^{2}}}{\left(1 - \left(e^{x^{2}} + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{6 x^{2} \left(e^{x^{2}} + 1\right)^{2} e^{2 x^{2}} \operatorname{asin}^{2}{\left(e^{x^{2}} + 1 \right)}}{\left(1 - \left(e^{x^{2}} + 1\right)^{2}\right)^{\frac{5}{2}}} - \frac{6 e^{x^{2}} \operatorname{asin}{\left(e^{x^{2}} + 1 \right)}}{\left(e^{x^{2}} + 1\right)^{2} - 1} + \frac{3 \operatorname{asin}^{2}{\left(e^{x^{2}} + 1 \right)}}{\sqrt{1 - \left(e^{x^{2}} + 1\right)^{2}}} + \frac{3 \left(e^{x^{2}} + 1\right) e^{x^{2}} \operatorname{asin}^{2}{\left(e^{x^{2}} + 1 \right)}}{\left(1 - \left(e^{x^{2}} + 1\right)^{2}\right)^{\frac{3}{2}}}\right) e^{x^{2}}
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Gráfico
Derivada de y=arcsin^3(1+e^x^2)
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