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

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

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

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Solución

Ha introducido [src] 
atan(2*x)
---------
       2 
  1 - x
atan⁡(2x)1−x2\frac{\operatorname{atan}{\left(2 x \right)}}{1 - x^{2}} 
atan(2*x)/(1 - x^2)
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         2            2*x*atan(2*x)
------------------- + -------------
/     2\ /       2\             2  
\1 - x /*\1 + 4*x /     /     2\   
                        \1 - x /
2xatan⁡(2x)(1−x2)2+2(1−x2)(4x2+1)\frac{2 x \operatorname{atan}{\left(2 x \right)}}{\left(1 - x^{2}\right)^{2}} + \frac{2}{\left(1 - x^{2}\right) \left(4 x^{2} + 1\right)}
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Segunda derivada [src] 
  /              /          2 \                                 \
  |              |       4*x  |                                 |
  |              |-1 + -------|*atan(2*x)                       |
  |              |           2|                                 |
  |    8*x       \     -1 + x /                     4*x         |
2*|----------- - ------------------------ + --------------------|
  |          2                 2            /       2\ /      2\|
  |/       2\            -1 + x             \1 + 4*x /*\-1 + x /|
  \\1 + 4*x /                                                   /
-----------------------------------------------------------------
                                   2                             
                             -1 + x
2(8x(4x2+1)2+4x(x2−1)(4x2+1)−(4x2x2−1−1)atan⁡(2x)x2−1)x2−1\frac{2 \left(\frac{8 x}{\left(4 x^{2} + 1\right)^{2}} + \frac{4 x}{\left(x^{2} - 1\right) \left(4 x^{2} + 1\right)} - \frac{\left(\frac{4 x^{2}}{x^{2} - 1} - 1\right) \operatorname{atan}{\left(2 x \right)}}{x^{2} - 1}\right)}{x^{2} - 1}
Simplificar
Tercera derivada [src] 
  /    /          2  \                               /          2 \         /          2 \          \
  |    |      16*x   |                               |       4*x  |         |       2*x  |          |
  |  4*|-1 + --------|                             3*|-1 + -------|     6*x*|-1 + -------|*atan(2*x)|
  |    |            2|               2               |           2|         |           2|          |
  |    \     1 + 4*x /           24*x                \     -1 + x /         \     -1 + x /          |
4*|- ----------------- - --------------------- - -------------------- + ----------------------------|
  |               2                2             /       2\ /      2\                     2         |
  |     /       2\       /       2\  /      2\   \1 + 4*x /*\-1 + x /            /      2\          |
  \     \1 + 4*x /       \1 + 4*x / *\-1 + x /                                   \-1 + x /          /
-----------------------------------------------------------------------------------------------------
                                                     2                                               
                                               -1 + x
4(−24x2(x2−1)(4x2+1)2+6x(2x2x2−1−1)atan⁡(2x)(x2−1)2−4(16x24x2+1−1)(4x2+1)2−3(4x2x2−1−1)(x2−1)(4x2+1))x2−1\frac{4 \left(- \frac{24 x^{2}}{\left(x^{2} - 1\right) \left(4 x^{2} + 1\right)^{2}} + \frac{6 x \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right) \operatorname{atan}{\left(2 x \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{4 \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right)}{\left(4 x^{2} + 1\right)^{2}} - \frac{3 \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right) \left(4 x^{2} + 1\right)}\right)}{x^{2} - 1}
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Gráfico
Derivada de atan(2*x)/(1-x^2)
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