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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   
$$\frac{\operatorname{atan}{\left(2 x + 1 \right)}}{2 x - 1}$$
atan(2*x + 1)/(2*x - 1)
Gráfica
Primera derivada [src]
  2*atan(2*x + 1)               2             
- --------------- + --------------------------
              2     /             2\          
     (2*x - 1)      \1 + (2*x + 1) /*(2*x - 1)
$$\frac{2}{\left(2 x - 1\right) \left(\left(2 x + 1\right)^{2} + 1\right)} - \frac{2 \operatorname{atan}{\left(2 x + 1 \right)}}{\left(2 x - 1\right)^{2}}$$
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                             
$$\frac{8 \left(- \frac{2 x + 1}{\left(\left(2 x + 1\right)^{2} + 1\right)^{2}} - \frac{1}{\left(2 x - 1\right) \left(\left(2 x + 1\right)^{2} + 1\right)} + \frac{\operatorname{atan}{\left(2 x + 1 \right)}}{\left(2 x - 1\right)^{2}}\right)}{2 x - 1}$$
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                                                
$$\frac{16 \left(\frac{\frac{4 \left(2 x + 1\right)^{2}}{\left(2 x + 1\right)^{2} + 1} - 1}{\left(\left(2 x + 1\right)^{2} + 1\right)^{2}} + \frac{3 \left(2 x + 1\right)}{\left(2 x - 1\right) \left(\left(2 x + 1\right)^{2} + 1\right)^{2}} + \frac{3}{\left(2 x - 1\right)^{2} \left(\left(2 x + 1\right)^{2} + 1\right)} - \frac{3 \operatorname{atan}{\left(2 x + 1 \right)}}{\left(2 x - 1\right)^{3}}\right)}{2 x - 1}$$
Gráfico
Derivada de atan(2*x+1)/(2*x-1)