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y=(arctqx)^3x
Derivada de la función/ y=(arctqx)^3x

Derivada de y=(arctqx)^3x

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

Gráfico:

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Solución

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