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atan(2*x/(1-x^2))
Derivada de la función/ 1-x^2/ atan(2*x/(1-x^2))

Derivada de atan(2*x/(1-x^2))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    / 2*x  \
atan|------|
    |     2|
    \1 - x /
atan⁡(2x1−x2)\operatorname{atan}{\left(\frac{2 x}{1 - x^{2}} \right)} 
atan((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(1−x2)2+21−x24x2(1−x2)2+1\frac{\frac{4 x^{2}}{\left(1 - x^{2}\right)^{2}} + \frac{2}{1 - x^{2}}}{\frac{4 x^{2}}{\left(1 - x^{2}\right)^{2}} + 1}
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Segunda derivada [src] 
    /                                  2     \
    |                    /          2 \      |
    |                    |       2*x  |      |
    |                  4*|-1 + -------|      |
    |         2          |           2|      |
    |      4*x           \     -1 + x /      |
4*x*|3 - ------- + --------------------------|
    |          2   /          2   \          |
    |    -1 + x    |       4*x    | /      2\|
    |              |1 + ----------|*\-1 + x /|
    |              |             2|          |
    |              |    /      2\ |          |
    \              \    \-1 + x / /          /
----------------------------------------------
         /          2   \          2          
         |       4*x    | /      2\           
         |1 + ----------|*\-1 + x /           
         |             2|                     
         |    /      2\ |                     
         \    \-1 + x / /
4x(−4x2x2−1+3+4(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{4 \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} \left(\frac{4 x^{2}}{\left(x^{2} - 1\right)^{2}} + 1\right)}
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Tercera derivada [src] 
  /                             /          2 \ /         2          4   \                          3                                          \
  |                             |       2*x  | |     10*x       12*x    |            /          2 \              /          2 \ /          2 \|
  |                           4*|-1 + -------|*|1 - ------- + ----------|          2 |       2*x  |            2 |       2*x  | |       4*x  ||
  |                             |           2| |          2            2|      64*x *|-1 + -------|        16*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\             |       4*x    | /      2\           /          2   \           3       |       4*x    | /      2\     |
  |              \-1 + x /             |1 + ----------|*\-1 + x /           |       4*x    |  /      2\        |1 + ----------|*\-1 + x /     |
  |                                    |             2|                     |1 + ----------| *\-1 + x /        |             2|               |
  |                                    |    /      2\ |                     |             2|                   |    /      2\ |               |
  |                                    \    \-1 + x / /                     |    /      2\ |                   \    \-1 + x / /               |
  \                                                                         \    \-1 + x / /                                                  /
-----------------------------------------------------------------------------------------------------------------------------------------------
                                                          /          2   \          2                                                          
                                                          |       4*x    | /      2\                                                           
                                                          |1 + ----------|*\-1 + x /                                                           
                                                          |             2|                                                                     
                                                          |    /      2\ |                                                                     
                                                          \    \-1 + x / /
4(24x4(x2−1)2−24x2x2−1−16x2(2x2x2−1−1)(4x2x2−1−3)(x2−1)2(4x2(x2−1)2+1)+64x2(2x2x2−1−1)3(x2−1)3(4x2(x2−1)2+1)2+3−4(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{16 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{64 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{4 \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} \left(\frac{4 x^{2}}{\left(x^{2} - 1\right)^{2}} + 1\right)}
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Gráfico
Derivada de atan(2*x/(1-x^2))
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