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y=ln(arctg2x)/x
Derivada de la función/ ctg2x/ arctg/ y=ln(arctg2x)/x

Derivada de y=ln(arctg2x)/x

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

Gráfico:

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Solución

Ha introducido [src] 
log(atan(2*x))
--------------
      x
log⁡(atan⁡(2x))x\frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x} 
log(atan(2*x))/x
Gráfica
02468-8-6-4-2-1010500-250
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Trazar el gráfico f'(x)
Primera derivada [src] 
  log(atan(2*x))             2           
- -------------- + ----------------------
         2           /       2\          
        x          x*\1 + 4*x /*atan(2*x)
2x(4x2+1)atan⁡(2x)−log⁡(atan⁡(2x))x2\frac{2}{x \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{2}}
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Segunda derivada [src] 
  /                                             /    1          \ \
  |                                           2*|--------- + 4*x| |
  |log(atan(2*x))             2                 \atan(2*x)      / |
2*|-------------- - ---------------------- - ---------------------|
  |       2           /       2\                       2          |
  |      x          x*\1 + 4*x /*atan(2*x)   /       2\           |
  \                                          \1 + 4*x / *atan(2*x)/
-------------------------------------------------------------------
                                 x
2(−2(4x+1atan⁡(2x))(4x2+1)2atan⁡(2x)−2x(4x2+1)atan⁡(2x)+log⁡(atan⁡(2x))x2)x\frac{2 \left(- \frac{2 \left(4 x + \frac{1}{\operatorname{atan}{\left(2 x \right)}}\right)}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} - \frac{2}{x \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{2}}\right)}{x}
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Tercera derivada [src] 
  /                                                 /                                  2                         \                          \
  |                                                 |               1              16*x              6*x         |                          |
  |                                               8*|-1 + --------------------- + -------- + --------------------|       /    1          \  |
  |                                                 |     /       2\     2               2   /       2\          |     6*|--------- + 4*x|  |
  |  3*log(atan(2*x))              6                \     \1 + 4*x /*atan (2*x)   1 + 4*x    \1 + 4*x /*atan(2*x)/       \atan(2*x)      /  |
2*|- ---------------- + ----------------------- + ---------------------------------------------------------------- + -----------------------|
  |          3           2 /       2\                                            2                                               2          |
  |         x           x *\1 + 4*x /*atan(2*x)                        /       2\                                      /       2\           |
  \                                                                    \1 + 4*x / *atan(2*x)                         x*\1 + 4*x / *atan(2*x)/
---------------------------------------------------------------------------------------------------------------------------------------------
                                                                      x
2(8(16x24x2+1+6x(4x2+1)atan⁡(2x)−1+1(4x2+1)atan⁡2(2x))(4x2+1)2atan⁡(2x)+6(4x+1atan⁡(2x))x(4x2+1)2atan⁡(2x)+6x2(4x2+1)atan⁡(2x)−3log⁡(atan⁡(2x))x3)x\frac{2 \left(\frac{8 \left(\frac{16 x^{2}}{4 x^{2} + 1} + \frac{6 x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - 1 + \frac{1}{\left(4 x^{2} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)}}\right)}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{6 \left(4 x + \frac{1}{\operatorname{atan}{\left(2 x \right)}}\right)}{x \left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{6}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{3 \log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{3}}\right)}{x}
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Gráfico
Derivada de y=ln(arctg2x)/x
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