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y=x/2+arcsin((4-x^2)/(4+x^2))
Derivada de la función/ (4-x^2)/(4+x^2)/ y=x/2+arcsin((4-x^2)/(4+x^2))

Derivada de y=x/2+arcsin((4-x^2)/(4+x^2))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
        /     2\
x       |4 - x |
- + asin|------|
2       |     2|
        \4 + x /
x2+asin⁡(4−x2x2+4)\frac{x}{2} + \operatorname{asin}{\left(\frac{4 - x^{2}}{x^{2} + 4} \right)} 
x/2 + asin((4 - x^2)/(4 + x^2))
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                   /     2\
       2*x     2*x*\4 - x /
    - ------ - ------------
           2            2  
      4 + x     /     2\   
1               \4 + x /   
- + -----------------------
2           _______________
           /             2 
          /      /     2\  
         /       \4 - x /  
        /    1 - --------- 
       /                 2 
      /          /     2\  
    \/           \4 + x /
12+−2x(4−x2)(x2+4)2−2xx2+4−(4−x2)2(x2+4)2+1\frac{1}{2} + \frac{- \frac{2 x \left(4 - x^{2}\right)}{\left(x^{2} + 4\right)^{2}} - \frac{2 x}{x^{2} + 4}}{\sqrt{- \frac{\left(4 - x^{2}\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1}}
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Segunda derivada [src] 
   /                                                           2          \
   |                                             /           2\           |
   |                                           2 |     -4 + x |  /      2\|
   |                                        2*x *|-1 + -------| *\-4 + x /|
   |          2       2       2 /      2\        |           2|           |
   |    -4 + x     4*x     4*x *\-4 + x /        \      4 + x /           |
-2*|1 - ------- - ------ + -------------- + ------------------------------|
   |          2        2             2        /            2\             |
   |     4 + x    4 + x      /     2\         |    /     2\ |         2   |
   |                         \4 + x /         |    \4 - x / | /     2\    |
   |                                          |1 - ---------|*\4 + x /    |
   |                                          |            2|             |
   |                                          |    /     2\ |             |
   \                                          \    \4 + x / /             /
---------------------------------------------------------------------------
                              _______________                              
                             /             2                               
                            /      /     2\                                
                           /       \4 - x /   /     2\                     
                          /    1 - --------- *\4 + x /                     
                         /                 2                               
                        /          /     2\                                
                      \/           \4 + x /
−2(4x2(x2−4)(x2+4)2+2x2(x2−4)(x2−4x2+4−1)2(x2+4)2(−(4−x2)2(x2+4)2+1)−4x2x2+4−x2−4x2+4+1)(x2+4)−(4−x2)2(x2+4)2+1- \frac{2 \left(\frac{4 x^{2} \left(x^{2} - 4\right)}{\left(x^{2} + 4\right)^{2}} + \frac{2 x^{2} \left(x^{2} - 4\right) \left(\frac{x^{2} - 4}{x^{2} + 4} - 1\right)^{2}}{\left(x^{2} + 4\right)^{2} \left(- \frac{\left(4 - x^{2}\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)} - \frac{4 x^{2}}{x^{2} + 4} - \frac{x^{2} - 4}{x^{2} + 4} + 1\right)}{\left(x^{2} + 4\right) \sqrt{- \frac{\left(4 - x^{2}\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1}}
Simplificar
Tercera derivada [src] 
    /                                                            /                     2                                  2\                                                                                                       \
    |                                             /           2\ |            /      2\       2 /      2\      2 /      2\ |     /           2\           /          2       2       2 /      2\\                      3           |
    |                                             |     -4 + x | |        2   \-4 + x /    8*x *\-4 + x /   6*x *\-4 + x / |     |     -4 + x | /      2\ |    -4 + x     4*x     4*x *\-4 + x /|        /           2\           2|
    |                                             |-1 + -------|*|-4 + 3*x  - ---------- - -------------- + ---------------|   2*|-1 + -------|*\-4 + x /*|1 - ------- - ------ + --------------|      2 |     -4 + x |  /      2\ |
    |                                             |           2| |                   2              2                  2   |     |           2|           |          2        2             2   |   6*x *|-1 + -------| *\-4 + x / |
    |        2      /      2\       2 /      2\   \      4 + x / |              4 + x          4 + x           /     2\    |     \      4 + x /           |     4 + x    4 + x      /     2\    |        |           2|            |
    |    12*x     6*\-4 + x /   12*x *\-4 + x /                  \                                             \4 + x /    /                              \                         \4 + x /    /        \      4 + x /            |
4*x*|6 - ------ - ----------- + --------------- + -------------------------------------------------------------------------- + ------------------------------------------------------------------ + -------------------------------|
    |         2           2                2                               /            2\                                                          /            2\                                                   2            |
    |    4 + x       4 + x         /     2\                                |    /     2\ |                                                          |    /     2\ |                                    /            2\             |
    |                              \4 + x /                                |    \4 - x / | /     2\                                                 |    \4 - x / | /     2\                           |    /     2\ |          3  |
    |                                                                      |1 - ---------|*\4 + x /                                                 |1 - ---------|*\4 + x /                           |    \4 - x / |  /     2\   |
    |                                                                      |            2|                                                          |            2|                                    |1 - ---------| *\4 + x /   |
    |                                                                      |    /     2\ |                                                          |    /     2\ |                                    |            2|             |
    |                                                                      \    \4 + x / /                                                          \    \4 + x / /                                    |    /     2\ |             |
    \                                                                                                                                                                                                  \    \4 + x / /             /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                         _______________                                                                                                            
                                                                                                        /             2                                                                                                             
                                                                                                       /      /     2\           2                                                                                                  
                                                                                                      /       \4 - x /   /     2\                                                                                                   
                                                                                                     /    1 - --------- *\4 + x /                                                                                                   
                                                                                                    /                 2                                                                                                             
                                                                                                   /          /     2\                                                                                                              
                                                                                                 \/           \4 + x /
4x(6x2(x2−4)2(x2−4x2+4−1)3(x2+4)3(−(4−x2)2(x2+4)2+1)2+12x2(x2−4)(x2+4)2−12x2x2+4−6(x2−4)x2+4+2(x2−4)(x2−4x2+4−1)(4x2(x2−4)(x2+4)2−4x2x2+4−x2−4x2+4+1)(x2+4)(−(4−x2)2(x2+4)2+1)+6+(x2−4x2+4−1)(6x2(x2−4)2(x2+4)2−8x2(x2−4)x2+4+3x2−(x2−4)2x2+4−4)(x2+4)(−(4−x2)2(x2+4)2+1))(x2+4)2−(4−x2)2(x2+4)2+1\frac{4 x \left(\frac{6 x^{2} \left(x^{2} - 4\right)^{2} \left(\frac{x^{2} - 4}{x^{2} + 4} - 1\right)^{3}}{\left(x^{2} + 4\right)^{3} \left(- \frac{\left(4 - x^{2}\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)^{2}} + \frac{12 x^{2} \left(x^{2} - 4\right)}{\left(x^{2} + 4\right)^{2}} - \frac{12 x^{2}}{x^{2} + 4} - \frac{6 \left(x^{2} - 4\right)}{x^{2} + 4} + \frac{2 \left(x^{2} - 4\right) \left(\frac{x^{2} - 4}{x^{2} + 4} - 1\right) \left(\frac{4 x^{2} \left(x^{2} - 4\right)}{\left(x^{2} + 4\right)^{2}} - \frac{4 x^{2}}{x^{2} + 4} - \frac{x^{2} - 4}{x^{2} + 4} + 1\right)}{\left(x^{2} + 4\right) \left(- \frac{\left(4 - x^{2}\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)} + 6 + \frac{\left(\frac{x^{2} - 4}{x^{2} + 4} - 1\right) \left(\frac{6 x^{2} \left(x^{2} - 4\right)^{2}}{\left(x^{2} + 4\right)^{2}} - \frac{8 x^{2} \left(x^{2} - 4\right)}{x^{2} + 4} + 3 x^{2} - \frac{\left(x^{2} - 4\right)^{2}}{x^{2} + 4} - 4\right)}{\left(x^{2} + 4\right) \left(- \frac{\left(4 - x^{2}\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1\right)}\right)}{\left(x^{2} + 4\right)^{2} \sqrt{- \frac{\left(4 - x^{2}\right)^{2}}{\left(x^{2} + 4\right)^{2}} + 1}}
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Gráfico
Derivada de y=x/2+arcsin((4-x^2)/(4+x^2))
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