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y=arcctgx/2-arctg6x²
Derivada de la función/ tgx/2/ ctg6x/ arctg/ y=arcctgx/ y=arcctgx/2-arctg6x/ y=arcctgx/2-arctg6x²

Derivada de y=arcctgx/2-arctg6x²

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
acot(x)       2     
------- - atan (6*x)
   2
acot⁡(x)2−atan⁡2(6x)\frac{\operatorname{acot}{\left(x \right)}}{2} - \operatorname{atan}^{2}{\left(6 x \right)} 
acot(x)/2 - atan(6*x)^2
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      1        12*atan(6*x)
- ---------- - ------------
    /     2\            2  
  2*\1 + x /    1 + 36*x
−12atan⁡(6x)36x2+1−12(x2+1)- \frac{12 \operatorname{atan}{\left(6 x \right)}}{36 x^{2} + 1} - \frac{1}{2 \left(x^{2} + 1\right)}
Simplificar
Segunda derivada [src] 
       72            x       864*x*atan(6*x)
- ------------ + --------- + ---------------
             2           2                2 
  /        2\    /     2\      /        2\  
  \1 + 36*x /    \1 + x /      \1 + 36*x /
864xatan⁡(6x)(36x2+1)2+x(x2+1)2−72(36x2+1)2\frac{864 x \operatorname{atan}{\left(6 x \right)}}{\left(36 x^{2} + 1\right)^{2}} + \frac{x}{\left(x^{2} + 1\right)^{2}} - \frac{72}{\left(36 x^{2} + 1\right)^{2}}
Simplificar
Tercera derivada [src] 
                  2                                            2          
    1          4*x      864*atan(6*x)     15552*x      124416*x *atan(6*x)
--------- - --------- + ------------- + ------------ - -------------------
        2           3               2              3                  3   
/     2\    /     2\     /        2\    /        2\        /        2\    
\1 + x /    \1 + x /     \1 + 36*x /    \1 + 36*x /        \1 + 36*x /
−124416x2atan⁡(6x)(36x2+1)3−4x2(x2+1)3+15552x(36x2+1)3+864atan⁡(6x)(36x2+1)2+1(x2+1)2- \frac{124416 x^{2} \operatorname{atan}{\left(6 x \right)}}{\left(36 x^{2} + 1\right)^{3}} - \frac{4 x^{2}}{\left(x^{2} + 1\right)^{3}} + \frac{15552 x}{\left(36 x^{2} + 1\right)^{3}} + \frac{864 \operatorname{atan}{\left(6 x \right)}}{\left(36 x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right)^{2}}
Simplificar
Gráfico
Derivada de y=arcctgx/2-arctg6x²
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