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y=x*arсctgx/2-x*arctg6x^2
Derivada de la función/ tgx/2/ ctg6x/ arctg/ y=x*arсctgx/2-x*arctg6x^2

Derivada de y=x*arсctgx/2-x*arctg6x^2

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

Gráfico:

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Solución

Ha introducido [src] 
x*acot(x)         2     
--------- - x*atan (6*x)
    2
−xatan⁡2(6x)+xacot⁡(x)2- x \operatorname{atan}^{2}{\left(6 x \right)} + \frac{x \operatorname{acot}{\left(x \right)}}{2} 
(x*acot(x))/2 - x*atan(6*x)^2
Gráfica
02468-8-6-4-2-1010-5050
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Trazar el gráfico f'(x)
Primera derivada [src] 
acot(x)       2            x        12*x*atan(6*x)
------- - atan (6*x) - ---------- - --------------
   2                     /     2\             2   
                       2*\1 + x /     1 + 36*x
−12xatan⁡(6x)36x2+1−x2(x2+1)+acot⁡(x)2−atan⁡2(6x)- \frac{12 x \operatorname{atan}{\left(6 x \right)}}{36 x^{2} + 1} - \frac{x}{2 \left(x^{2} + 1\right)} + \frac{\operatorname{acot}{\left(x \right)}}{2} - \operatorname{atan}^{2}{\left(6 x \right)}
Simplificar
Segunda derivada [src] 
                2                                         2          
    1          x           72*x       24*atan(6*x)   864*x *atan(6*x)
- ------ + --------- - ------------ - ------------ + ----------------
       2           2              2            2                  2  
  1 + x    /     2\    /        2\     1 + 36*x        /        2\   
           \1 + x /    \1 + 36*x /                     \1 + 36*x /
864x2atan⁡(6x)(36x2+1)2+x2(x2+1)2−72x(36x2+1)2−24atan⁡(6x)36x2+1−1x2+1\frac{864 x^{2} \operatorname{atan}{\left(6 x \right)}}{\left(36 x^{2} + 1\right)^{2}} + \frac{x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{72 x}{\left(36 x^{2} + 1\right)^{2}} - \frac{24 \operatorname{atan}{\left(6 x \right)}}{36 x^{2} + 1} - \frac{1}{x^{2} + 1}
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Tercera derivada [src] 
  /                                  3              2             3                            \
  |       54            x           x         3888*x       31104*x *atan(6*x)   864*x*atan(6*x)|
4*|- ------------ + --------- - --------- + ------------ - ------------------ + ---------------|
  |             2           2           3              3                 3                   2 |
  |  /        2\    /     2\    /     2\    /        2\       /        2\         /        2\  |
  \  \1 + 36*x /    \1 + x /    \1 + x /    \1 + 36*x /       \1 + 36*x /         \1 + 36*x /  /
4(−31104x3atan⁡(6x)(36x2+1)3−x3(x2+1)3+3888x2(36x2+1)3+864xatan⁡(6x)(36x2+1)2+x(x2+1)2−54(36x2+1)2)4 \left(- \frac{31104 x^{3} \operatorname{atan}{\left(6 x \right)}}{\left(36 x^{2} + 1\right)^{3}} - \frac{x^{3}}{\left(x^{2} + 1\right)^{3}} + \frac{3888 x^{2}}{\left(36 x^{2} + 1\right)^{3}} + \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{54}{\left(36 x^{2} + 1\right)^{2}}\right)
Simplificar
Gráfico
Derivada de y=x*arсctgx/2-x*arctg6x^2
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