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x+(x-1)acrsin(sqrt(x/(x+1)))
Derivada de la función/ x+(x-1)acrsin(sqrt(x/(x+1)))

Derivada de x+(x-1)acrsin(sqrt(x/(x+1)))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                /    _______\
                |   /   x   |
x + (x - 1)*asin|  /  ----- |
                \\/   x + 1 /
x+(x−1)asin⁡(xx+1)x + \left(x - 1\right) \operatorname{asin}{\left(\sqrt{\frac{x}{x + 1}} \right)} 
x + (x - 1)*asin(sqrt(x/(x + 1)))
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        _______                                                             
       /   x                    /    1           x     \                    
      /  ----- *(x + 1)*(x - 1)*|--------- - ----------|                    
    \/   x + 1                  |2*(x + 1)            2|       /    _______\
                                \            2*(x + 1) /       |   /   x   |
1 + ---------------------------------------------------- + asin|  /  ----- |
                           ___________                         \\/   x + 1 /
                          /       x                                         
                     x*  /  1 - -----                                       
                       \/       x + 1
asin⁡(xx+1)+1+xx+1(x−1)(x+1)(−x2(x+1)2+12(x+1))x−xx+1+1\operatorname{asin}{\left(\sqrt{\frac{x}{x + 1}} \right)} + 1 + \frac{\sqrt{\frac{x}{x + 1}} \left(x - 1\right) \left(x + 1\right) \left(- \frac{x}{2 \left(x + 1\right)^{2}} + \frac{1}{2 \left(x + 1\right)}\right)}{x \sqrt{- \frac{x}{x + 1} + 1}}
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Segunda derivada [src] 
                         /                                   /       x  \            /       x  \\
    _______              |                          (-1 + x)*|-1 + -----|   (-1 + x)*|-1 + -----||
   /   x    /       x  \ |     -1 + x     -1 + x             \     1 + x/            \     1 + x/|
  /  ----- *|-1 + -----|*|-1 + ------ + --------- + --------------------- + ---------------------|
\/   1 + x  \     1 + x/ |      2*x     2*(1 + x)            4*x                      /      x  \|
                         |                                                  4*(1 + x)*|1 - -----||
                         \                                                            \    1 + x//
--------------------------------------------------------------------------------------------------
                                              ___________                                         
                                             /       x                                            
                                        x*  /  1 - -----                                          
                                          \/       1 + x
xx+1(xx+1−1)(x−12(x+1)+(x−1)(xx+1−1)4(x+1)(−xx+1+1)−1+(x−1)(xx+1−1)4x+x−12x)x−xx+1+1\frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right) \left(\frac{x - 1}{2 \left(x + 1\right)} + \frac{\left(x - 1\right) \left(\frac{x}{x + 1} - 1\right)}{4 \left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)} - 1 + \frac{\left(x - 1\right) \left(\frac{x}{x + 1} - 1\right)}{4 x} + \frac{x - 1}{2 x}\right)}{x \sqrt{- \frac{x}{x + 1} + 1}}
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Tercera derivada [src] 
                         /                                                                                                         2                                                                                                    2                                                   2         \
                         |                                        /       x  \                          /       x  \   /       x  \                   /       x  \               /       x  \              /       x  \     /       x  \                       /       x  \     /       x  \          |
    _______              |                                      3*|-1 + -----|               3*(-1 + x)*|-1 + -----|   |-1 + -----| *(-1 + x)       3*|-1 + -----|      (-1 + x)*|-1 + -----|   3*(-1 + x)*|-1 + -----|   3*|-1 + -----| *(-1 + x)    (-1 + x)*|-1 + -----|     |-1 + -----| *(-1 + x)|
   /   x    /       x  \ | 3        3       -1 + x    -1 + x      \     1 + x/     -1 + x               \     1 + x/   \     1 + x/                   \     1 + x/               \     1 + x/              \     1 + x/     \     1 + x/                       \     1 + x/     \     1 + x/          |
  /  ----- *|-1 + -----|*|--- + --------- - ------ - -------- + -------------- - --------- - ----------------------- - ---------------------- + --------------------- - --------------------- - ----------------------- - ------------------------ - ----------------------- - -----------------------|
\/   1 + x  \     1 + x/ |2*x   2*(1 + x)      2            2        4*x         x*(1 + x)                2                        2                      /      x  \           2 /      x  \         4*x*(1 + x)                               2                /      x  \               /      x  \|
                         |                    x      (1 + x)                                           4*x                      8*x             4*(1 + x)*|1 - -----|    (1 + x) *|1 - -----|                                      2 /      x  \     2*x*(1 + x)*|1 - -----|   4*x*(1 + x)*|1 - -----||
                         |                                                                                                                                \    1 + x/             \    1 + x/                             8*(1 + x) *|1 - -----|                 \    1 + x/               \    1 + x/|
                         \                                                                                                                                                                                                           \    1 + x/                                                      /
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                                                                                                                                                /       x                                                                                                                                              
                                                                                                                                           x*  /  1 - -----                                                                                                                                            
                                                                                                                                             \/       1 + x
xx+1(xx+1−1)(−x−1(x+1)2−(x−1)(xx+1−1)(x+1)2(−xx+1+1)−3(x−1)(xx+1−1)28(x+1)2(−xx+1+1)2+32(x+1)+3(xx+1−1)4(x+1)(−xx+1+1)−3(x−1)(xx+1−1)4x(x+1)−x−1x(x+1)−(x−1)(xx+1−1)24x(x+1)(−xx+1+1)−(x−1)(xx+1−1)2x(x+1)(−xx+1+1)+3(xx+1−1)4x+32x−(x−1)(xx+1−1)28x2−3(x−1)(xx+1−1)4x2−x−1x2)x−xx+1+1\frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right) \left(- \frac{x - 1}{\left(x + 1\right)^{2}} - \frac{\left(x - 1\right) \left(\frac{x}{x + 1} - 1\right)}{\left(x + 1\right)^{2} \left(- \frac{x}{x + 1} + 1\right)} - \frac{3 \left(x - 1\right) \left(\frac{x}{x + 1} - 1\right)^{2}}{8 \left(x + 1\right)^{2} \left(- \frac{x}{x + 1} + 1\right)^{2}} + \frac{3}{2 \left(x + 1\right)} + \frac{3 \left(\frac{x}{x + 1} - 1\right)}{4 \left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)} - \frac{3 \left(x - 1\right) \left(\frac{x}{x + 1} - 1\right)}{4 x \left(x + 1\right)} - \frac{x - 1}{x \left(x + 1\right)} - \frac{\left(x - 1\right) \left(\frac{x}{x + 1} - 1\right)^{2}}{4 x \left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)} - \frac{\left(x - 1\right) \left(\frac{x}{x + 1} - 1\right)}{2 x \left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)} + \frac{3 \left(\frac{x}{x + 1} - 1\right)}{4 x} + \frac{3}{2 x} - \frac{\left(x - 1\right) \left(\frac{x}{x + 1} - 1\right)^{2}}{8 x^{2}} - \frac{3 \left(x - 1\right) \left(\frac{x}{x + 1} - 1\right)}{4 x^{2}} - \frac{x - 1}{x^{2}}\right)}{x \sqrt{- \frac{x}{x + 1} + 1}}
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Gráfico
Derivada de x+(x-1)acrsin(sqrt(x/(x+1)))
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