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y=(2sqrt(1-x)arcsin(sqrtx))/x+2/sqrtxx*exp(-x)
Derivada de la función/ y=(2sqrt(1-x)arcsin(sqrtx))/x+2/sqrtxx*exp(-x)

Derivada de y=(2sqrt(1-x)arcsin(sqrtx))/x+2/sqrtxx*exp(-x)

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

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Solución

Ha introducido [src] 
    _______     /  ___\              
2*\/ 1 - x *asin\\/ x /      2     -x
----------------------- + -------*e  
           x                _____    
                          \/ x*x
2xxe−x+21−xasin⁡(x)x\frac{2}{\sqrt{x x}} e^{- x} + \frac{2 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}}{x} 
((2*sqrt(1 - x))*asin(sqrt(x)))/x + (2/sqrt(x*x))*exp(-x)
Primera derivada [src] 
            /  ___\                                            
  1     asin\\/ x /                                            
----- - -----------                                            
  ___      _______        -x       -x       _______     /  ___\
\/ x     \/ 1 - x      2*e      2*e     2*\/ 1 - x *asin\\/ x /
------------------- - ------- - ----- - -----------------------
         x               ____   x*|x|               2          
                        /  2                       x           
                      \/  x
−2e−x∣x∣+−asin⁡(x)1−x+1xx−2e−xx∣x∣−21−xasin⁡(x)x2- \frac{2 e^{- x}}{\left|{x}\right|} + \frac{- \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\sqrt{1 - x}} + \frac{1}{\sqrt{x}}}{x} - \frac{2 e^{- x}}{x \left|{x}\right|} - \frac{2 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{2}}
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Segunda derivada [src] 
                       /  ___\                      /  ___\                                                                                           
             1     asin\\/ x /            1     asin\\/ x /         1                                                                                 
         - ----- + -----------           ---- + ----------- - --------------                                                                          
             ___      _______       -x    3/2           3/2     ___                /  ___\       -x              -x       -x       _______     /  ___\
   1       \/ x     \/ 1 - x     2*e     x       (1 - x)      \/ x *(-1 + x)   asin\\/ x /    2*e  *sign(x)   2*e      4*e     4*\/ 1 - x *asin\\/ x /
- ---- + --------------------- + ----- - ----------------------------------- + ------------ + ------------- + ------ + ----- + -----------------------
   5/2              2             |x|                    2*x                    2   _______          3         2       x*|x|               3          
  x                x                                                           x *\/ 1 - x          x         x *|x|                      x
2e−x∣x∣−asin⁡(x)(1−x)32−1x(x−1)+1x322x+4e−xx∣x∣+asin⁡(x)1−x−1xx2+2e−xx2∣x∣+asin⁡(x)x21−x+41−xasin⁡(x)x3+2e−xsign⁡(x)x3−1x52\frac{2 e^{- x}}{\left|{x}\right|} - \frac{\frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\left(1 - x\right)^{\frac{3}{2}}} - \frac{1}{\sqrt{x} \left(x - 1\right)} + \frac{1}{x^{\frac{3}{2}}}}{2 x} + \frac{4 e^{- x}}{x \left|{x}\right|} + \frac{\frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\sqrt{1 - x}} - \frac{1}{\sqrt{x}}}{x^{2}} + \frac{2 e^{- x}}{x^{2} \left|{x}\right|} + \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{x^{2} \sqrt{1 - x}} + \frac{4 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{3}} + \frac{2 e^{- x} \operatorname{sign}{\left(x \right)}}{x^{3}} - \frac{1}{x^{\frac{5}{2}}}
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Tercera derivada [src] 
                    /  ___\                      /              /  ___\\                                                                              /  ___\                                                                                                                                                             
          1     asin\\/ x /         1            |    1     asin\\/ x /|                                3           1                3          3*asin\\/ x /                                                                                                                                                             
         ---- + ----------- - --------------   2*|- ----- + -----------|                             - ---- + ------------- + --------------- + -------------                                                                                                                                                             
          3/2           3/2     ___              |    ___      _______ |      -x                        5/2    3/2              ___         2            5/2          /  ___\          _______     /  ___\      -x              -x              -x       -x         /  ___\      -x       -x                            -x
  9      x       (1 - x)      \/ x *(-1 + x)     \  \/ x     \/ 1 - x  /   2*e            1            x      x   *(-1 + x)   \/ x *(-1 + x)      (1 - x)         asin\\/ x /     12*\/ 1 - x *asin\\/ x /   8*e  *sign(x)   6*e  *sign(x)   6*e      4*e     4*asin\\/ x /   4*e      2*e  *sign(x)   4*DiracDelta(x)*e  
------ + ----------------------------------- - ------------------------- - ----- - --------------- - -------------------------------------------------------- + --------------- - ------------------------ - ------------- - ------------- - ------ - ----- - ------------- - ------ - ------------- + -------------------
   7/2                     2                                3               |x|       5/2                                      4*x                                 2        3/2               4                     4               3         2       x*|x|     3   _______    3              2                  3        
2*x                       x                                x                       2*x   *(-1 + x)                                                              2*x *(1 - x)                 x                     x               x         x *|x|            x *\/ 1 - x    x *|x|         x                  x
−2e−x∣x∣−3asin⁡(x)(1−x)52+3x(x−1)2+1x32(x−1)−3x524x−4e−xx∣x∣+asin⁡(x)(1−x)32−1x(x−1)+1x32x2−2e−xsign⁡(x)x2−6e−xx2∣x∣+asin⁡(x)2x2(1−x)32−2(asin⁡(x)1−x−1x)x3+4e−xδ(x)x3−6e−xsign⁡(x)x3−4e−xx3∣x∣−4asin⁡(x)x31−x−121−xasin⁡(x)x4−8e−xsign⁡(x)x4−12x52(x−1)+92x72- \frac{2 e^{- x}}{\left|{x}\right|} - \frac{\frac{3 \operatorname{asin}{\left(\sqrt{x} \right)}}{\left(1 - x\right)^{\frac{5}{2}}} + \frac{3}{\sqrt{x} \left(x - 1\right)^{2}} + \frac{1}{x^{\frac{3}{2}} \left(x - 1\right)} - \frac{3}{x^{\frac{5}{2}}}}{4 x} - \frac{4 e^{- x}}{x \left|{x}\right|} + \frac{\frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\left(1 - x\right)^{\frac{3}{2}}} - \frac{1}{\sqrt{x} \left(x - 1\right)} + \frac{1}{x^{\frac{3}{2}}}}{x^{2}} - \frac{2 e^{- x} \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{6 e^{- x}}{x^{2} \left|{x}\right|} + \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{2 x^{2} \left(1 - x\right)^{\frac{3}{2}}} - \frac{2 \left(\frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\sqrt{1 - x}} - \frac{1}{\sqrt{x}}\right)}{x^{3}} + \frac{4 e^{- x} \delta\left(x\right)}{x^{3}} - \frac{6 e^{- x} \operatorname{sign}{\left(x \right)}}{x^{3}} - \frac{4 e^{- x}}{x^{3} \left|{x}\right|} - \frac{4 \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{3} \sqrt{1 - x}} - \frac{12 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{4}} - \frac{8 e^{- x} \operatorname{sign}{\left(x \right)}}{x^{4}} - \frac{1}{2 x^{\frac{5}{2}} \left(x - 1\right)} + \frac{9}{2 x^{\frac{7}{2}}}
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Gráfico
Derivada de y=(2sqrt(1-x)arcsin(sqrtx))/x+2/sqrtxx*exp(-x)
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