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

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

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

Gráfico:

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Solución

Ha introducido [src] 
atan(2*x + 1)
-------------
   2*x - 1
atan⁡(2x+1)2x−1\frac{\operatorname{atan}{\left(2 x + 1 \right)}}{2 x - 1} 
atan(2*x + 1)/(2*x - 1)
Gráfica
02468-8-6-4-2-1010-2500025000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  2*atan(2*x + 1)               2             
- --------------- + --------------------------
              2     /             2\          
     (2*x - 1)      \1 + (2*x + 1) /*(2*x - 1)
2(2x−1)((2x+1)2+1)−2atan⁡(2x+1)(2x−1)2\frac{2}{\left(2 x - 1\right) \left(\left(2 x + 1\right)^{2} + 1\right)} - \frac{2 \operatorname{atan}{\left(2 x + 1 \right)}}{\left(2 x - 1\right)^{2}}
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Segunda derivada [src] 
  /atan(1 + 2*x)                1                     1 + 2*x     \
8*|------------- - --------------------------- - -----------------|
  |           2    /             2\                              2|
  | (-1 + 2*x)     \1 + (1 + 2*x) /*(-1 + 2*x)   /             2\ |
  \                                              \1 + (1 + 2*x) / /
-------------------------------------------------------------------
                              -1 + 2*x
8(−2x+1((2x+1)2+1)2−1(2x−1)((2x+1)2+1)+atan⁡(2x+1)(2x−1)2)2x−1\frac{8 \left(- \frac{2 x + 1}{\left(\left(2 x + 1\right)^{2} + 1\right)^{2}} - \frac{1}{\left(2 x - 1\right) \left(\left(2 x + 1\right)^{2} + 1\right)} + \frac{\operatorname{atan}{\left(2 x + 1 \right)}}{\left(2 x - 1\right)^{2}}\right)}{2 x - 1}
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Tercera derivada [src] 
   /                 2                                                                                 \
   |      4*(1 + 2*x)                                                                                  |
   |-1 + --------------                                                                                |
   |                  2                                                                                |
   |     1 + (1 + 2*x)    3*atan(1 + 2*x)                3                         3*(1 + 2*x)         |
16*|------------------- - --------------- + ---------------------------- + ----------------------------|
   |                 2                3     /             2\           2                   2           |
   | /             2\       (-1 + 2*x)      \1 + (1 + 2*x) /*(-1 + 2*x)    /             2\            |
   \ \1 + (1 + 2*x) /                                                      \1 + (1 + 2*x) / *(-1 + 2*x)/
--------------------------------------------------------------------------------------------------------
                                                -1 + 2*x
16(4(2x+1)2(2x+1)2+1−1((2x+1)2+1)2+3(2x+1)(2x−1)((2x+1)2+1)2+3(2x−1)2((2x+1)2+1)−3atan⁡(2x+1)(2x−1)3)2x−1\frac{16 \left(\frac{\frac{4 \left(2 x + 1\right)^{2}}{\left(2 x + 1\right)^{2} + 1} - 1}{\left(\left(2 x + 1\right)^{2} + 1\right)^{2}} + \frac{3 \left(2 x + 1\right)}{\left(2 x - 1\right) \left(\left(2 x + 1\right)^{2} + 1\right)^{2}} + \frac{3}{\left(2 x - 1\right)^{2} \left(\left(2 x + 1\right)^{2} + 1\right)} - \frac{3 \operatorname{atan}{\left(2 x + 1 \right)}}{\left(2 x - 1\right)^{3}}\right)}{2 x - 1}
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Gráfico
Derivada de atan(2*x+1)/(2*x-1)
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