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

Derivada de y=ln(arctg2x)

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

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Solución

Ha introducido [src] 
log(atan(2*x))
$$\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}$$ 
log(atan(2*x))
Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         2          
--------------------
/       2\          
\1 + 4*x /*atan(2*x)
$$\frac{2}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}$$
Simplificar
Segunda derivada [src] 
    /    1          \
 -4*|--------- + 4*x|
    \atan(2*x)      /
---------------------
          2          
/       2\           
\1 + 4*x / *atan(2*x)
$$- \frac{4 \left(4 x + \frac{1}{\operatorname{atan}{\left(2 x \right)}}\right)}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}}$$
Simplificar
Tercera derivada [src] 
   /                                  2                         \
   |               1              16*x              6*x         |
16*|-1 + --------------------- + -------- + --------------------|
   |     /       2\     2               2   /       2\          |
   \     \1 + 4*x /*atan (2*x)   1 + 4*x    \1 + 4*x /*atan(2*x)/
-----------------------------------------------------------------
                                2                                
                      /       2\                                 
                      \1 + 4*x / *atan(2*x)
$$\frac{16 \left(\frac{16 x^{2}}{4 x^{2} + 1} + \frac{6 x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - 1 + \frac{1}{\left(4 x^{2} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)}}\right)}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}}$$
Simplificar
Gráfico
Derivada de y=ln(arctg2x)
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