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Derivada de x*sin(|x|)+x/(1+x^2)

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

Ha introducido [src]
               x   
x*sin(|x|) + ------
                  2
             1 + x 
$$x \sin{\left(\left|{x}\right| \right)} + \frac{x}{x^{2} + 1}$$
x*sin(|x|) + x/(1 + x^2)
Primera derivada [src]
               2                                  
  1         2*x                                   
------ - --------- + x*cos(|x|)*sign(x) + sin(|x|)
     2           2                                
1 + x    /     2\                                 
         \1 + x /                                 
$$- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} + x \cos{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)} + \sin{\left(\left|{x}\right| \right)} + \frac{1}{x^{2} + 1}$$
Segunda derivada [src]
                                         3                                                     
     6*x                              8*x            2                                         
- --------- + 2*cos(|x|)*sign(x) + --------- - x*sign (x)*sin(|x|) + 2*x*DiracDelta(x)*cos(|x|)
          2                                3                                                   
  /     2\                         /     2\                                                    
  \1 + x /                         \1 + x /                                                    
$$\frac{8 x^{3}}{\left(x^{2} + 1\right)^{3}} - x \sin{\left(\left|{x}\right| \right)} \operatorname{sign}^{2}{\left(x \right)} + 2 x \cos{\left(\left|{x}\right| \right)} \delta\left(x\right) - \frac{6 x}{\left(x^{2} + 1\right)^{2}} + 2 \cos{\left(\left|{x}\right| \right)} \operatorname{sign}{\left(x \right)}$$
Tercera derivada [src]
                    4                                                            2                                                                                             
      6         48*x            2                                            48*x            3                                                                                 
- --------- - --------- - 3*sign (x)*sin(|x|) + 6*DiracDelta(x)*cos(|x|) + --------- - x*sign (x)*cos(|x|) + 2*x*DiracDelta(x, 1)*cos(|x|) - 6*x*DiracDelta(x)*sign(x)*sin(|x|)
          2           4                                                            3                                                                                           
  /     2\    /     2\                                                     /     2\                                                                                            
  \1 + x /    \1 + x /                                                     \1 + x /                                                                                            
$$- \frac{48 x^{4}}{\left(x^{2} + 1\right)^{4}} + \frac{48 x^{2}}{\left(x^{2} + 1\right)^{3}} - 6 x \sin{\left(\left|{x}\right| \right)} \delta\left(x\right) \operatorname{sign}{\left(x \right)} + 2 x \cos{\left(\left|{x}\right| \right)} \delta^{\left( 1 \right)}\left( x \right) - x \cos{\left(\left|{x}\right| \right)} \operatorname{sign}^{3}{\left(x \right)} - 3 \sin{\left(\left|{x}\right| \right)} \operatorname{sign}^{2}{\left(x \right)} + 6 \cos{\left(\left|{x}\right| \right)} \delta\left(x\right) - \frac{6}{\left(x^{2} + 1\right)^{2}}$$