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acos(sqrt(1+x^2))^3+e^(-x^2)
Derivada de la función/ acos(sqrt(1+x^2))^3+e^(-x^2)

Derivada de acos(sqrt(1+x^2))^3+e^(-x^2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     /   ________\      2
    3|  /      2 |    -x 
acos \\/  1 + x  / + E
acos⁡3(x2+1)+e−x2\operatorname{acos}^{3}{\left(\sqrt{x^{2} + 1} \right)} + e^{- x^{2}} 
acos(sqrt(1 + x^2))^3 + E^(-x^2)
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    3*I*x*acos \\/  1 + x  /
- 2*x*e    + ------------------------
                    ________         
                   /      2          
                 \/  1 + x  *|x|
−2xe−x2+3ixacos⁡2(x2+1)x2+1∣x∣- 2 x e^{- x^{2}} + \frac{3 i x \operatorname{acos}^{2}{\left(\sqrt{x^{2} + 1} \right)}}{\sqrt{x^{2} + 1} \left|{x}\right|}
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Segunda derivada [src] 
                 /   ________\                        /   ________\            /   ________\                       /   ________\
       2         |  /      2 |           2           2|  /      2 |           2|  /      2 |                2     2|  /      2 |
     -x    6*acos\\/  1 + x  /      2  -x    3*I*acos \\/  1 + x  /   3*I*acos \\/  1 + x  /*sign(x)   3*I*x *acos \\/  1 + x  /
- 2*e    - ------------------- + 4*x *e    + ---------------------- - ------------------------------ - -------------------------
                       2                           ________                        ________                         3/2         
                  1 + x                           /      2                        /      2                  /     2\            
                                                \/  1 + x  *|x|               x*\/  1 + x                   \1 + x /   *|x|
4x2e−x2−3ix2acos⁡2(x2+1)(x2+1)32∣x∣−2e−x2−6acos⁡(x2+1)x2+1+3iacos⁡2(x2+1)x2+1∣x∣−3iacos⁡2(x2+1)sign⁡(x)xx2+14 x^{2} e^{- x^{2}} - \frac{3 i x^{2} \operatorname{acos}^{2}{\left(\sqrt{x^{2} + 1} \right)}}{\left(x^{2} + 1\right)^{\frac{3}{2}} \left|{x}\right|} - 2 e^{- x^{2}} - \frac{6 \operatorname{acos}{\left(\sqrt{x^{2} + 1} \right)}}{x^{2} + 1} + \frac{3 i \operatorname{acos}^{2}{\left(\sqrt{x^{2} + 1} \right)}}{\sqrt{x^{2} + 1} \left|{x}\right|} - \frac{3 i \operatorname{acos}^{2}{\left(\sqrt{x^{2} + 1} \right)} \operatorname{sign}{\left(x \right)}}{x \sqrt{x^{2} + 1}}
Simplificar
Tercera derivada [src] 
                                /   ________\            /   ________\                              /   ________\                 /   ________\                      /   ________\            /   ________\                             /   ________\
          2           2         |  /      2 |            |  /      2 |                             2|  /      2 |                 |  /      2 |                     2|  /      2 |           2|  /      2 |                      3     2|  /      2 |
     3  -x          -x    6*acos\\/  1 + x  /   18*x*acos\\/  1 + x  /        6*I*x        6*I*acos \\/  1 + x  /*sign(x)   6*acos\\/  1 + x  /*sign(x)   9*I*x*acos \\/  1 + x  /   6*I*acos \\/  1 + x  /*DiracDelta(x)   9*I*x *acos \\/  1 + x  /
- 8*x *e    + 12*x*e    - ------------------- + ---------------------- - --------------- + ------------------------------ + --------------------------- - ------------------------ - ------------------------------------ + -------------------------
                                 /     2\                     2                  3/2                        3/2                     /     2\                          3/2                            ________                            5/2         
                               x*\1 + x /             /     2\           /     2\                   /     2\                        \1 + x /*|x|              /     2\                              /      2                     /     2\            
                                                      \1 + x /           \1 + x /   *|x|            \1 + x /                                                  \1 + x /   *|x|                   x*\/  1 + x                      \1 + x /   *|x|
−8x3e−x2+9ix3acos⁡2(x2+1)(x2+1)52∣x∣+12xe−x2+18xacos⁡(x2+1)(x2+1)2−9ixacos⁡2(x2+1)(x2+1)32∣x∣−6ix(x2+1)32∣x∣+6acos⁡(x2+1)sign⁡(x)(x2+1)∣x∣+6iacos⁡2(x2+1)sign⁡(x)(x2+1)32−6acos⁡(x2+1)x(x2+1)−6iδ(x)acos⁡2(x2+1)xx2+1- 8 x^{3} e^{- x^{2}} + \frac{9 i x^{3} \operatorname{acos}^{2}{\left(\sqrt{x^{2} + 1} \right)}}{\left(x^{2} + 1\right)^{\frac{5}{2}} \left|{x}\right|} + 12 x e^{- x^{2}} + \frac{18 x \operatorname{acos}{\left(\sqrt{x^{2} + 1} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{9 i x \operatorname{acos}^{2}{\left(\sqrt{x^{2} + 1} \right)}}{\left(x^{2} + 1\right)^{\frac{3}{2}} \left|{x}\right|} - \frac{6 i x}{\left(x^{2} + 1\right)^{\frac{3}{2}} \left|{x}\right|} + \frac{6 \operatorname{acos}{\left(\sqrt{x^{2} + 1} \right)} \operatorname{sign}{\left(x \right)}}{\left(x^{2} + 1\right) \left|{x}\right|} + \frac{6 i \operatorname{acos}^{2}{\left(\sqrt{x^{2} + 1} \right)} \operatorname{sign}{\left(x \right)}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} - \frac{6 \operatorname{acos}{\left(\sqrt{x^{2} + 1} \right)}}{x \left(x^{2} + 1\right)} - \frac{6 i \delta\left(x\right) \operatorname{acos}^{2}{\left(\sqrt{x^{2} + 1} \right)}}{x \sqrt{x^{2} + 1}}
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Gráfico
Derivada de acos(sqrt(1+x^2))^3+e^(-x^2)
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