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

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

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    /    _______\
    |   / 1 - x |
asin|  /  ----- |
    \\/   1 + x /
asin⁡(1−xx+1)\operatorname{asin}{\left(\sqrt{\frac{1 - x}{x + 1}} \right)} 
asin(sqrt((1 - x)/(1 + x)))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    _______                                   
   / 1 - x          /      1         1 - x   \
  /  ----- *(1 + x)*|- --------- - ----------|
\/   1 + x          |  2*(1 + x)            2|
                    \              2*(1 + x) /
----------------------------------------------
                       ___________            
                      /     1 - x             
           (1 - x)*  /  1 - -----             
                   \/       1 + x
1−xx+1(x+1)(−1−x2(x+1)2−12(x+1))(1−x)−1−xx+1+1\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 \left(x + 1\right)}\right)}{\left(1 - x\right) \sqrt{- \frac{1 - x}{x + 1} + 1}}
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Segunda derivada [src] 
                               /                      -1 + x            -1 + x    \
    ____________               |                 -1 + ------       -1 + ------    |
   / -(-1 + x)   /     -1 + x\ |  2       2           1 + x             1 + x     |
  /  ---------- *|-1 + ------|*|----- + ------ + ----------- - -------------------|
\/     1 + x     \     1 + x / |1 + x   -1 + x      -1 + x             /    1 - x\|
                               |                               (1 + x)*|1 - -----||
                               \                                       \    1 + x//
-----------------------------------------------------------------------------------
                                   ___________                                     
                                  /     1 - x                                      
                             4*  /  1 - ----- *(-1 + x)                            
                               \/       1 + x
−x−1x+1(x−1x+1−1)(2x+1−x−1x+1−1(x+1)(−1−xx+1+1)+x−1x+1−1x−1+2x−1)4(x−1)−1−xx+1+1\frac{\sqrt{- \frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right) \left(\frac{2}{x + 1} - \frac{\frac{x - 1}{x + 1} - 1}{\left(x + 1\right) \left(- \frac{1 - x}{x + 1} + 1\right)} + \frac{\frac{x - 1}{x + 1} - 1}{x - 1} + \frac{2}{x - 1}\right)}{4 \left(x - 1\right) \sqrt{- \frac{1 - x}{x + 1} + 1}}
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Tercera derivada [src] 
                               /                                                                           2                                                                  2                                                            2        \
                               |                                              /     -1 + x\   /     -1 + x\             -1 + x           /     -1 + x\           /     -1 + x\                     -1 + x                     /     -1 + x\         |
    ____________               |                                            3*|-1 + ------|   |-1 + ------|        -1 + ------         3*|-1 + ------|         3*|-1 + ------|                -1 + ------                     |-1 + ------|         |
   / -(-1 + x)   /     -1 + x\ |     1           1              1             \     1 + x /   \     1 + x /             1 + x            \     1 + x /           \     1 + x /                     1 + x                      \     1 + x /         |
  /  ---------- *|-1 + ------|*|- -------- - --------- - ---------------- - --------------- - -------------- + -------------------- - ------------------ - ----------------------- + ------------------------------ + ------------------------------|
\/     1 + x     \     1 + x / |         2           2   (1 + x)*(-1 + x)               2                2            2 /    1 - x\   4*(1 + x)*(-1 + x)                         2             /    1 - x\                      /    1 - x\         |
                               |  (1 + x)    (-1 + x)                         4*(-1 + x)       8*(-1 + x)      (1 + x) *|1 - -----|                                 2 /    1 - x\    2*(1 + x)*|1 - -----|*(-1 + x)   4*(1 + x)*|1 - -----|*(-1 + x)|
                               |                                                                                        \    1 + x/                        8*(1 + x) *|1 - -----|              \    1 + x/                      \    1 + x/         |
                               \                                                                                                                                      \    1 + x/                                                                   /
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                                                                                                                   ___________                                                                                                                       
                                                                                                                  /     1 - x                                                                                                                        
                                                                                                                 /  1 - ----- *(-1 + x)                                                                                                              
                                                                                                               \/       1 + x
−x−1x+1(x−1x+1−1)(−1(x+1)2+x−1x+1−1(x+1)2(−1−xx+1+1)−3(x−1x+1−1)28(x+1)2(−1−xx+1+1)2−3(x−1x+1−1)4(x−1)(x+1)−1(x−1)(x+1)+(x−1x+1−1)24(x−1)(x+1)(−1−xx+1+1)+x−1x+1−12(x−1)(x+1)(−1−xx+1+1)−(x−1x+1−1)28(x−1)2−3(x−1x+1−1)4(x−1)2−1(x−1)2)(x−1)−1−xx+1+1\frac{\sqrt{- \frac{x - 1}{x + 1}} \left(\frac{x - 1}{x + 1} - 1\right) \left(- \frac{1}{\left(x + 1\right)^{2}} + \frac{\frac{x - 1}{x + 1} - 1}{\left(x + 1\right)^{2} \left(- \frac{1 - x}{x + 1} + 1\right)} - \frac{3 \left(\frac{x - 1}{x + 1} - 1\right)^{2}}{8 \left(x + 1\right)^{2} \left(- \frac{1 - x}{x + 1} + 1\right)^{2}} - \frac{3 \left(\frac{x - 1}{x + 1} - 1\right)}{4 \left(x - 1\right) \left(x + 1\right)} - \frac{1}{\left(x - 1\right) \left(x + 1\right)} + \frac{\left(\frac{x - 1}{x + 1} - 1\right)^{2}}{4 \left(x - 1\right) \left(x + 1\right) \left(- \frac{1 - x}{x + 1} + 1\right)} + \frac{\frac{x - 1}{x + 1} - 1}{2 \left(x - 1\right) \left(x + 1\right) \left(- \frac{1 - x}{x + 1} + 1\right)} - \frac{\left(\frac{x - 1}{x + 1} - 1\right)^{2}}{8 \left(x - 1\right)^{2}} - \frac{3 \left(\frac{x - 1}{x + 1} - 1\right)}{4 \left(x - 1\right)^{2}} - \frac{1}{\left(x - 1\right)^{2}}\right)}{\left(x - 1\right) \sqrt{- \frac{1 - x}{x + 1} + 1}}
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Gráfico
Derivada de y=arcsin(sqrt((1-x)/(1+x)))
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