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xsinx-arctg^3x
Derivada de la función/ tg^3x/ arctg/ xsinx/ xsinx-arctg^3x

Derivada de xsinx-arctg^3x

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

Gráfico:

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Solución

Ha introducido [src] 
               3   
x*sin(x) - atan (x)
xsin⁡(x)−atan⁡3(x)x \sin{\left(x \right)} - \operatorname{atan}^{3}{\left(x \right)} 
x*sin(x) - atan(x)^3
Gráfica
02468-8-6-4-2-1010-2525
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Trazar el gráfico f'(x)
Primera derivada [src] 
                 2            
           3*atan (x)         
x*cos(x) - ---------- + sin(x)
                  2           
             1 + x
xcos⁡(x)+sin⁡(x)−3atan⁡2(x)x2+1x \cos{\left(x \right)} + \sin{\left(x \right)} - \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
                                          2   
                      6*atan(x)   6*x*atan (x)
2*cos(x) - x*sin(x) - --------- + ------------
                              2            2  
                      /     2\     /     2\   
                      \1 + x /     \1 + x /
−xsin⁡(x)+6xatan⁡2(x)(x2+1)2+2cos⁡(x)−6atan⁡(x)(x2+1)2- x \sin{\left(x \right)} + \frac{6 x \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + 2 \cos{\left(x \right)} - \frac{6 \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}
Simplificar
Tercera derivada [src] 
                                          2          2     2                  
      6                             6*atan (x)   24*x *atan (x)   36*x*atan(x)
- --------- - 3*sin(x) - x*cos(x) + ---------- - -------------- + ------------
          3                                 2              3               3  
  /     2\                          /     2\       /     2\        /     2\   
  \1 + x /                          \1 + x /       \1 + x /        \1 + x /
−24x2atan⁡2(x)(x2+1)3−xcos⁡(x)+36xatan⁡(x)(x2+1)3−3sin⁡(x)+6atan⁡2(x)(x2+1)2−6(x2+1)3- \frac{24 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - x \cos{\left(x \right)} + \frac{36 x \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - 3 \sin{\left(x \right)} + \frac{6 \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6}{\left(x^{2} + 1\right)^{3}}
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Gráfico
Derivada de xsinx-arctg^3x
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