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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    _______     /  ___\        
2*\/ 1 - x *asin\\/ x /     2  
----------------------- + -----
           x                ___
                          \/ x
21−xasin⁡(x)x+2x\frac{2 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}}{x} + \frac{2}{\sqrt{x}} 
((2*sqrt(1 - x))*asin(sqrt(x)))/x + 2/sqrt(x)
Gráfica
02468-8-6-4-2-1010-100100
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Primera derivada [src] 
                     /  ___\                          
           1     asin\\/ x /                          
         ----- - -----------                          
           ___      _______        _______     /  ___\
   1     \/ x     \/ 1 - x     2*\/ 1 - x *asin\\/ x /
- ---- + ------------------- - -----------------------
   3/2            x                        2          
  x                                       x
−asin⁡(x)1−x+1xx−21−xasin⁡(x)x2−1x32\frac{- \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\sqrt{1 - x}} + \frac{1}{\sqrt{x}}}{x} - \frac{2 \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{2}} - \frac{1}{x^{\frac{3}{2}}}
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Segunda derivada [src] 
                       /  ___\              /  ___\                                                          
             1     asin\\/ x /    1     asin\\/ x /         1                                                
         - ----- + -----------   ---- + ----------- - --------------                                         
             ___      _______     3/2           3/2     ___                /  ___\        _______     /  ___\
  1        \/ x     \/ 1 - x     x       (1 - x)      \/ x *(-1 + x)   asin\\/ x /    4*\/ 1 - x *asin\\/ x /
------ + --------------------- - ----------------------------------- + ------------ + -----------------------
   5/2              2                            2*x                    2   _______               3          
2*x                x                                                   x *\/ 1 - x               x
−asin⁡(x)(1−x)32−1x(x−1)+1x322x+asin⁡(x)1−x−1xx2+asin⁡(x)x21−x+41−xasin⁡(x)x3+12x52- \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{\frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\sqrt{1 - x}} - \frac{1}{\sqrt{x}}}{x^{2}} + \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{1}{2 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     ___              |    ___      _______ |                        5/2    3/2              ___         2            5/2          /  ___\          _______     /  ___\         /  ___\
  3      x       (1 - x)      \/ x *(-1 + x)     \  \/ x     \/ 1 - x  /          1            x      x   *(-1 + x)   \/ x *(-1 + x)      (1 - x)         asin\\/ x /     12*\/ 1 - x *asin\\/ x /   4*asin\\/ x /
------ + ----------------------------------- - ------------------------- - --------------- - -------------------------------------------------------- + --------------- - ------------------------ - -------------
   7/2                     2                                3                 5/2                                      4*x                                 2        3/2               4                3   _______
4*x                       x                                x               2*x   *(-1 + x)                                                              2*x *(1 - x)                 x                x *\/ 1 - x
−3asin⁡(x)(1−x)52+3x(x−1)2+1x32(x−1)−3x524x+asin⁡(x)(1−x)32−1x(x−1)+1x32x2+asin⁡(x)2x2(1−x)32−2(asin⁡(x)1−x−1x)x3−4asin⁡(x)x31−x−121−xasin⁡(x)x4−12x52(x−1)+34x72- \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{\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{\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 \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{1}{2 x^{\frac{5}{2}} \left(x - 1\right)} + \frac{3}{4 x^{\frac{7}{2}}}
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Gráfico
Derivada de y=(2sqrt(1-x)arcsin(sqrtx))/x+2/sqrtx
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