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arcsin(2x/(1+x^2))
Derivada de la función/ 1+x^2/ arcsin/ arcsin(2x/(1+x^2))

Derivada de arcsin(2x/(1+x^2))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    / 2*x  \
asin|------|
    |     2|
    \1 + x /
asin⁡(2xx2+1)\operatorname{asin}{\left(\frac{2 x}{x^{2} + 1} \right)} 
asin((2*x)/(1 + x^2))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                 2    
    2         4*x     
  ------ - ---------  
       2           2  
  1 + x    /     2\   
           \1 + x /   
----------------------
       _______________
      /           2   
     /         4*x    
    /   1 - --------- 
   /                2 
  /         /     2\  
\/          \1 + x /
−4x2(x2+1)2+2x2+1−4x2(x2+1)2+1\frac{- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2}{x^{2} + 1}}{\sqrt{- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1}}
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Segunda derivada [src] 
    /                                 2    \
    |                    /         2 \     |
    |                    |      2*x  |     |
    |                  2*|-1 + ------|     |
    |         2          |          2|     |
    |      4*x           \     1 + x /     |
4*x*|-3 + ------ + ------------------------|
    |          2            /          2  \|
    |     1 + x    /     2\ |       4*x   ||
    |              \1 + x /*|1 - ---------||
    |                       |            2||
    |                       |    /     2\ ||
    \                       \    \1 + x / //
--------------------------------------------
                       _______________      
              2       /           2         
      /     2\       /         4*x          
      \1 + x / *    /   1 - ---------       
                   /                2       
                  /         /     2\        
                \/          \1 + x /
4x(4x2x2+1−3+2(2x2x2+1−1)2(x2+1)(−4x2(x2+1)2+1))(x2+1)2−4x2(x2+1)2+1\frac{4 x \left(\frac{4 x^{2}}{x^{2} + 1} - 3 + \frac{2 \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right)^{2}}{\left(x^{2} + 1\right) \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1\right)}\right)}{\left(x^{2} + 1\right)^{2} \sqrt{- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1}}
Simplificar
Tercera derivada [src] 
   /                           /         2 \ /        2          4  \                         3                                      \
   |                           |      2*x  | |    10*x       12*x   |            /         2 \            /         2 \ /         2 \|
   |                         2*|-1 + ------|*|1 - ------ + ---------|          2 |      2*x  |          2 |      2*x  | |      4*x  ||
   |                           |          2| |         2           2|      24*x *|-1 + ------|       8*x *|-1 + ------|*|-3 + ------||
   |        2          4       \     1 + x / |    1 + x    /     2\ |            |          2|            |          2| |          2||
   |    24*x       24*x                      \             \1 + x / /            \     1 + x /            \     1 + x / \     1 + x /|
-4*|3 - ------ + --------- + ---------------------------------------- + -------------------------- + --------------------------------|
   |         2           2                    /          2  \                                    2              2 /          2  \    |
   |    1 + x    /     2\            /     2\ |       4*x   |                   3 /          2  \       /     2\  |       4*x   |    |
   |             \1 + x /            \1 + x /*|1 - ---------|           /     2\  |       4*x   |       \1 + x / *|1 - ---------|    |
   |                                          |            2|           \1 + x / *|1 - ---------|                 |            2|    |
   |                                          |    /     2\ |                     |            2|                 |    /     2\ |    |
   |                                          \    \1 + x / /                     |    /     2\ |                 \    \1 + x / /    |
   \                                                                              \    \1 + x / /                                    /
--------------------------------------------------------------------------------------------------------------------------------------
                                                                    _______________                                                   
                                                           2       /           2                                                      
                                                   /     2\       /         4*x                                                       
                                                   \1 + x / *    /   1 - ---------                                                    
                                                                /                2                                                    
                                                               /         /     2\                                                     
                                                             \/          \1 + x /
−4(24x4(x2+1)2−24x2x2+1+8x2(2x2x2+1−1)(4x2x2+1−3)(x2+1)2(−4x2(x2+1)2+1)+24x2(2x2x2+1−1)3(x2+1)3(−4x2(x2+1)2+1)2+3+2(2x2x2+1−1)(12x4(x2+1)2−10x2x2+1+1)(x2+1)(−4x2(x2+1)2+1))(x2+1)2−4x2(x2+1)2+1- \frac{4 \left(\frac{24 x^{4}}{\left(x^{2} + 1\right)^{2}} - \frac{24 x^{2}}{x^{2} + 1} + \frac{8 x^{2} \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 3\right)}{\left(x^{2} + 1\right)^{2} \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1\right)} + \frac{24 x^{2} \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right)^{3}}{\left(x^{2} + 1\right)^{3} \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1\right)^{2}} + 3 + \frac{2 \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \left(\frac{12 x^{4}}{\left(x^{2} + 1\right)^{2}} - \frac{10 x^{2}}{x^{2} + 1} + 1\right)}{\left(x^{2} + 1\right) \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1\right)}\right)}{\left(x^{2} + 1\right)^{2} \sqrt{- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1}}
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Gráfico
Derivada de arcsin(2x/(1+x^2))
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