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

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /  _______\
    |\/ 1 - x |
asin|---------|
    \  1 + x  /
asin⁡(1−xx+1)\operatorname{asin}{\left(\frac{\sqrt{1 - x}}{x + 1} \right)} 
asin(sqrt(1 - x)/(1 + x))
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
    _______                      
  \/ 1 - x             1         
- --------- - -------------------
          2               _______
   (1 + x)    2*(1 + x)*\/ 1 - x 
---------------------------------
            ______________       
           /      1 - x          
          /  1 - --------        
         /              2        
       \/        (1 + x)
−1−x(x+1)2−121−x(x+1)−1−x(x+1)2+1\frac{- \frac{\sqrt{1 - x}}{\left(x + 1\right)^{2}} - \frac{1}{2 \sqrt{1 - x} \left(x + 1\right)}}{\sqrt{- \frac{1 - x}{\left(x + 1\right)^{2}} + 1}}
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Segunda derivada [src] 
                                                                     /                _______\
                                                   /     2*(-1 + x)\ |    1       2*\/ 1 - x |
                                                   |-1 + ----------|*|--------- + -----------|
                                         _______   \       1 + x   / |  _______      1 + x   |
       1                 1           2*\/ 1 - x                      \\/ 1 - x               /
- ------------ + ----------------- + ----------- - -------------------------------------------
           3/2             _______            2                      2 /     1 - x  \         
  4*(1 - x)      (1 + x)*\/ 1 - x      (1 + x)              4*(1 + x) *|1 - --------|         
                                                                       |           2|         
                                                                       \    (1 + x) /         
----------------------------------------------------------------------------------------------
                                              ______________                                  
                                             /      1 - x                                     
                                 (1 + x)*   /  1 - --------                                   
                                           /              2                                   
                                         \/        (1 + x)
21−x(x+1)2−(21−xx+1+11−x)(2(x−1)x+1−1)4(x+1)2(−1−x(x+1)2+1)+11−x(x+1)−14(1−x)32(x+1)−1−x(x+1)2+1\frac{\frac{2 \sqrt{1 - x}}{\left(x + 1\right)^{2}} - \frac{\left(\frac{2 \sqrt{1 - x}}{x + 1} + \frac{1}{\sqrt{1 - x}}\right) \left(\frac{2 \left(x - 1\right)}{x + 1} - 1\right)}{4 \left(x + 1\right)^{2} \left(- \frac{1 - x}{\left(x + 1\right)^{2}} + 1\right)} + \frac{1}{\sqrt{1 - x} \left(x + 1\right)} - \frac{1}{4 \left(1 - x\right)^{\frac{3}{2}}}}{\left(x + 1\right) \sqrt{- \frac{1 - x}{\left(x + 1\right)^{2}} + 1}}
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Tercera derivada [src] 
                                                                                             /                _______\                      2 /                _______\                     /                                       _______\
                                                                           /     3*(-1 + x)\ |    1       2*\/ 1 - x |     /     2*(-1 + x)\  |    1       2*\/ 1 - x |   /     2*(-1 + x)\ |      1                4           8*\/ 1 - x |
                                                                           |-2 + ----------|*|--------- + -----------|   3*|-1 + ----------| *|--------- + -----------|   |-1 + ----------|*|- ---------- + ----------------- + -----------|
                     _______                                               \       1 + x   / |  _______      1 + x   |     \       1 + x   /  |  _______      1 + x   |   \       1 + x   / |         3/2             _______            2 |
       3         6*\/ 1 - x            3                     3                               \\/ 1 - x               /                        \\/ 1 - x               /                     \  (1 - x)      (1 + x)*\/ 1 - x      (1 + x)  /
- ------------ - ----------- - ------------------ + -------------------- + ------------------------------------------- - ---------------------------------------------- + ------------------------------------------------------------------
           5/2            3           2   _______                    3/2                     3 /     1 - x  \                                               2                                          2 /     1 - x  \                     
  8*(1 - x)        (1 + x)     (1 + x) *\/ 1 - x    4*(1 + x)*(1 - x)               2*(1 + x) *|1 - --------|                               4 /     1 - x  \                                  4*(1 + x) *|1 - --------|                     
                                                                                               |           2|                      8*(1 + x) *|1 - --------|                                             |           2|                     
                                                                                               \    (1 + x) /                                 |           2|                                             \    (1 + x) /                     
                                                                                                                                              \    (1 + x) /                                                                                
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                     ______________                                                                                                         
                                                                                                                    /      1 - x                                                                                                            
                                                                                                        (1 + x)*   /  1 - --------                                                                                                          
                                                                                                                  /              2                                                                                                          
                                                                                                                \/        (1 + x)
−61−x(x+1)3+(2(x−1)x+1−1)(81−x(x+1)2+41−x(x+1)−1(1−x)32)4(x+1)2(−1−x(x+1)2+1)+(21−xx+1+11−x)(3(x−1)x+1−2)2(x+1)3(−1−x(x+1)2+1)−3(21−xx+1+11−x)(2(x−1)x+1−1)28(x+1)4(−1−x(x+1)2+1)2−31−x(x+1)2+34(1−x)32(x+1)−38(1−x)52(x+1)−1−x(x+1)2+1\frac{- \frac{6 \sqrt{1 - x}}{\left(x + 1\right)^{3}} + \frac{\left(\frac{2 \left(x - 1\right)}{x + 1} - 1\right) \left(\frac{8 \sqrt{1 - x}}{\left(x + 1\right)^{2}} + \frac{4}{\sqrt{1 - x} \left(x + 1\right)} - \frac{1}{\left(1 - x\right)^{\frac{3}{2}}}\right)}{4 \left(x + 1\right)^{2} \left(- \frac{1 - x}{\left(x + 1\right)^{2}} + 1\right)} + \frac{\left(\frac{2 \sqrt{1 - x}}{x + 1} + \frac{1}{\sqrt{1 - x}}\right) \left(\frac{3 \left(x - 1\right)}{x + 1} - 2\right)}{2 \left(x + 1\right)^{3} \left(- \frac{1 - x}{\left(x + 1\right)^{2}} + 1\right)} - \frac{3 \left(\frac{2 \sqrt{1 - x}}{x + 1} + \frac{1}{\sqrt{1 - x}}\right) \left(\frac{2 \left(x - 1\right)}{x + 1} - 1\right)^{2}}{8 \left(x + 1\right)^{4} \left(- \frac{1 - x}{\left(x + 1\right)^{2}} + 1\right)^{2}} - \frac{3}{\sqrt{1 - x} \left(x + 1\right)^{2}} + \frac{3}{4 \left(1 - x\right)^{\frac{3}{2}} \left(x + 1\right)} - \frac{3}{8 \left(1 - x\right)^{\frac{5}{2}}}}{\left(x + 1\right) \sqrt{- \frac{1 - x}{\left(x + 1\right)^{2}} + 1}}
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Gráfico
Derivada de y=arcsin(sqrt(1-x)/(1+x))
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