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

Derivada de y=x*arcsin(sqrt(x)+sqrt(x-1))

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

Gráfico:

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Solución

Ha introducido [src] 
      /  ___     _______\
x*asin\\/ x  + \/ x - 1 /
xasin⁡(x+x−1)x \operatorname{asin}{\left(\sqrt{x} + \sqrt{x - 1} \right)} 
x*asin(sqrt(x) + sqrt(x - 1))
Gráfica
02468-8-6-4-2-10100.02-0.02
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    /   1           1     \                             
  x*|------- + -----------|                             
    |    ___       _______|                             
    \2*\/ x    2*\/ x - 1 /          /  ___     _______\
------------------------------ + asin\\/ x  + \/ x - 1 /
    __________________________                          
   /                        2                           
  /      /  ___     _______\                            
\/   1 - \\/ x  + \/ x - 1 /
x(12x−1+12x)1−(x+x−1)2+asin⁡(x+x−1)\frac{x \left(\frac{1}{2 \sqrt{x - 1}} + \frac{1}{2 \sqrt{x}}\right)}{\sqrt{1 - \left(\sqrt{x} + \sqrt{x - 1}\right)^{2}}} + \operatorname{asin}{\left(\sqrt{x} + \sqrt{x - 1} \right)}
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Segunda derivada [src] 
                       /                                         2                     \
                       |                     /  1         1     \  /  ___     ________\|
                       |                     |----- + ----------| *\\/ x  + \/ -1 + x /|
                       |                     |  ___     ________|                      |
                       | 1          1        \\/ x    \/ -1 + x /                      |
                     x*|---- + ----------- + ------------------------------------------|
                       | 3/2           3/2                                    2        |
                       |x      (-1 + x)                   /  ___     ________\         |
  1         1          \                             -1 + \\/ x  + \/ -1 + x /         /
----- + ---------- - -------------------------------------------------------------------
  ___     ________                                    4                                 
\/ x    \/ -1 + x                                                                       
----------------------------------------------------------------------------------------
                                ___________________________                             
                               /                         2                              
                              /      /  ___     ________\                               
                            \/   1 - \\/ x  + \/ -1 + x /
−x((x+x−1)(1x−1+1x)2(x+x−1)2−1+1(x−1)32+1x32)4+1x−1+1x1−(x+x−1)2\frac{- \frac{x \left(\frac{\left(\sqrt{x} + \sqrt{x - 1}\right) \left(\frac{1}{\sqrt{x - 1}} + \frac{1}{\sqrt{x}}\right)^{2}}{\left(\sqrt{x} + \sqrt{x - 1}\right)^{2} - 1} + \frac{1}{\left(x - 1\right)^{\frac{3}{2}}} + \frac{1}{x^{\frac{3}{2}}}\right)}{4} + \frac{1}{\sqrt{x - 1}} + \frac{1}{\sqrt{x}}}{\sqrt{1 - \left(\sqrt{x} + \sqrt{x - 1}\right)^{2}}}
Simplificar
Tercera derivada [src] 
                         /                                           3                            2                     3                                                                   \                         2                     
                         |                       /  1         1     \         /  ___     ________\  /  1         1     \      /  ___     ________\ / 1          1     \ /  1         1     \|     /  1         1     \  /  ___     ________\
                         |                       |----- + ----------|       3*\\/ x  + \/ -1 + x / *|----- + ----------|    3*\\/ x  + \/ -1 + x /*|---- + -----------|*|----- + ----------||   6*|----- + ----------| *\\/ x  + \/ -1 + x /
                         |                       |  ___     ________|                               |  ___     ________|                           | 3/2           3/2| |  ___     ________||     |  ___     ________|                      
   6          6          | 3          3          \\/ x    \/ -1 + x /                               \\/ x    \/ -1 + x /                           \x      (-1 + x)   / \\/ x    \/ -1 + x /|     \\/ x    \/ -1 + x /                      
- ---- - ----------- + x*|---- + ----------- - -------------------------- + --------------------------------------------- + ----------------------------------------------------------------| - --------------------------------------------
   3/2           3/2     | 5/2           5/2                            2                                       2                                                       2                   |                                     2         
  x      (-1 + x)        |x      (-1 + x)           /  ___     ________\            /                         2\                                    /  ___     ________\                    |                 /  ___     ________\          
                         |                     -1 + \\/ x  + \/ -1 + x /            |     /  ___     ________\ |                               -1 + \\/ x  + \/ -1 + x /                    |            -1 + \\/ x  + \/ -1 + x /          
                         \                                                          \-1 + \\/ x  + \/ -1 + x / /                                                                            /                                               
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                           ___________________________                                                                                                      
                                                                                                          /                         2                                                                                                       
                                                                                                         /      /  ___     ________\                                                                                                        
                                                                                                     8*\/   1 - \\/ x  + \/ -1 + x /
x(3(x+x−1)2(1x−1+1x)3((x+x−1)2−1)2+3(x+x−1)(1(x−1)32+1x32)(1x−1+1x)(x+x−1)2−1−(1x−1+1x)3(x+x−1)2−1+3(x−1)52+3x52)−6(x+x−1)(1x−1+1x)2(x+x−1)2−1−6(x−1)32−6x3281−(x+x−1)2\frac{x \left(\frac{3 \left(\sqrt{x} + \sqrt{x - 1}\right)^{2} \left(\frac{1}{\sqrt{x - 1}} + \frac{1}{\sqrt{x}}\right)^{3}}{\left(\left(\sqrt{x} + \sqrt{x - 1}\right)^{2} - 1\right)^{2}} + \frac{3 \left(\sqrt{x} + \sqrt{x - 1}\right) \left(\frac{1}{\left(x - 1\right)^{\frac{3}{2}}} + \frac{1}{x^{\frac{3}{2}}}\right) \left(\frac{1}{\sqrt{x - 1}} + \frac{1}{\sqrt{x}}\right)}{\left(\sqrt{x} + \sqrt{x - 1}\right)^{2} - 1} - \frac{\left(\frac{1}{\sqrt{x - 1}} + \frac{1}{\sqrt{x}}\right)^{3}}{\left(\sqrt{x} + \sqrt{x - 1}\right)^{2} - 1} + \frac{3}{\left(x - 1\right)^{\frac{5}{2}}} + \frac{3}{x^{\frac{5}{2}}}\right) - \frac{6 \left(\sqrt{x} + \sqrt{x - 1}\right) \left(\frac{1}{\sqrt{x - 1}} + \frac{1}{\sqrt{x}}\right)^{2}}{\left(\sqrt{x} + \sqrt{x - 1}\right)^{2} - 1} - \frac{6}{\left(x - 1\right)^{\frac{3}{2}}} - \frac{6}{x^{\frac{3}{2}}}}{8 \sqrt{1 - \left(\sqrt{x} + \sqrt{x - 1}\right)^{2}}}
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Gráfico
Derivada de y=x*arcsin(sqrt(x)+sqrt(x-1))
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