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y=arcctg(x/2)-arctg6x^2
Derivada de la función/ ctg6x/ (x/2)/ arctg/ y=arcctg(x/2)-arctg6x^2

Derivada de y=arcctg(x/2)-arctg6x^2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /x\       2     
acot|-| - atan (6*x)
    \2/
$$\operatorname{acot}{\left(\frac{x}{2} \right)} - \operatorname{atan}^{2}{\left(6 x \right)}$$ 
acot(x/2) - atan(6*x)^2
Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      1        12*atan(6*x)
- ---------- - ------------
    /     2\            2  
    |    x |    1 + 36*x   
  2*|1 + --|               
    \    4 /
$$- \frac{12 \operatorname{atan}{\left(6 x \right)}}{36 x^{2} + 1} - \frac{1}{2 \left(\frac{x^{2}}{4} + 1\right)}$$
Simplificar
Segunda derivada [src] 
  /       18            x       216*x*atan(6*x)\
4*|- ------------ + --------- + ---------------|
  |             2           2                2 |
  |  /        2\    /     2\      /        2\  |
  \  \1 + 36*x /    \4 + x /      \1 + 36*x /  /
$$4 \left(\frac{216 x \operatorname{atan}{\left(6 x \right)}}{\left(36 x^{2} + 1\right)^{2}} + \frac{x}{\left(x^{2} + 4\right)^{2}} - \frac{18}{\left(36 x^{2} + 1\right)^{2}}\right)$$
Simplificar
Tercera derivada [src] 
  /                  2                                           2          \
  |    1          4*x      216*atan(6*x)      3888*x      31104*x *atan(6*x)|
4*|--------- - --------- + ------------- + ------------ - ------------------|
  |        2           3               2              3                 3   |
  |/     2\    /     2\     /        2\    /        2\       /        2\    |
  \\4 + x /    \4 + x /     \1 + 36*x /    \1 + 36*x /       \1 + 36*x /    /
$$4 \left(- \frac{31104 x^{2} \operatorname{atan}{\left(6 x \right)}}{\left(36 x^{2} + 1\right)^{3}} - \frac{4 x^{2}}{\left(x^{2} + 4\right)^{3}} + \frac{3888 x}{\left(36 x^{2} + 1\right)^{3}} + \frac{216 \operatorname{atan}{\left(6 x \right)}}{\left(36 x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 4\right)^{2}}\right)$$
Simplificar
Gráfico
Derivada de y=arcctg(x/2)-arctg6x^2
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