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y=x*arctg(x)^2
Derivada de la función/ (x)^2/ tg(x)/ arctg/ y=x*arctg(x)^2

Derivada de y=x*arctg(x)^2

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

Gráfico:

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Solución

Ha introducido [src] 
      2   
x*atan (x)
xatan⁡2(x)x \operatorname{atan}^{2}{\left(x \right)} 
x*atan(x)^2
Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    2      2*x*atan(x)
atan (x) + -----------
                   2  
              1 + x
2xatan⁡(x)x2+1+atan⁡2(x)\frac{2 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \operatorname{atan}^{2}{\left(x \right)}
Simplificar
Segunda derivada [src] 
  /            x*(-1 + 2*x*atan(x))\
2*|2*atan(x) - --------------------|
  |                        2       |
  \                   1 + x        /
------------------------------------
                    2               
               1 + x
2(−x(2xatan⁡(x)−1)x2+1+2atan⁡(x))x2+1\frac{2 \left(- \frac{x \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{x^{2} + 1} + 2 \operatorname{atan}{\left(x \right)}\right)}{x^{2} + 1}
Simplificar
Tercera derivada [src] 
   /         /            2                  \              \
   |         | 3*x     4*x *atan(x)          |              |
-2*|-3 + 2*x*|------ - ------------ + atan(x)| + 6*x*atan(x)|
   |         |     2           2             |              |
   \         \1 + x       1 + x              /              /
-------------------------------------------------------------
                                  2                          
                          /     2\                           
                          \1 + x /
−2(2x(−4x2atan⁡(x)x2+1+3xx2+1+atan⁡(x))+6xatan⁡(x)−3)(x2+1)2- \frac{2 \left(2 x \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) + 6 x \operatorname{atan}{\left(x \right)} - 3\right)}{\left(x^{2} + 1\right)^{2}}
Simplificar
3-я производная [src] 
   /         /            2                  \              \
   |         | 3*x     4*x *atan(x)          |              |
-2*|-3 + 2*x*|------ - ------------ + atan(x)| + 6*x*atan(x)|
   |         |     2           2             |              |
   \         \1 + x       1 + x              /              /
-------------------------------------------------------------
                                  2                          
                          /     2\                           
                          \1 + x /
−2(2x(−4x2atan⁡(x)x2+1+3xx2+1+atan⁡(x))+6xatan⁡(x)−3)(x2+1)2- \frac{2 \left(2 x \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) + 6 x \operatorname{atan}{\left(x \right)} - 3\right)}{\left(x^{2} + 1\right)^{2}}
Simplificar
Gráfico
Derivada de y=x*arctg(x)^2
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