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Derivada de la función/ e^x^2/ x^2+sinx/ x|sinx|+e^x^2+sinx\x

Derivada de x|sinx|+e^x^2+sinx\x

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

Gráfico:

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Solución

Ha introducido [src] 
              / 2\         
              \x /   sin(x)
x*|sin(x)| + E     + ------
                       x
(ex2+x∣sin⁡(x)∣)+sin⁡(x)x\left(e^{x^{2}} + x \left|{\sin{\left(x \right)}}\right|\right) + \frac{\sin{\left(x \right)}}{x} 
x*Abs(sin(x)) + E^(x^2) + sin(x)/x
Primera derivada [src] 
                       / 2\                                   
cos(x)   sin(x)        \x /                                   
------ - ------ + 2*x*e     + x*cos(x)*sign(sin(x)) + |sin(x)|
  x         2                                                 
           x
2xex2+xcos⁡(x)sign⁡(sin⁡(x))+∣sin⁡(x)∣+cos⁡(x)x−sin⁡(x)x22 x e^{x^{2}} + x \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} + \left|{\sin{\left(x \right)}}\right| + \frac{\cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}
Simplificar
Segunda derivada [src] 
   / 2\                                                                / 2\                                                         
   \x /   sin(x)   2*cos(x)   2*sin(x)                              2  \x /                                  2                      
2*e     - ------ - -------- + -------- + 2*cos(x)*sign(sin(x)) + 4*x *e     - x*sign(sin(x))*sin(x) + 2*x*cos (x)*DiracDelta(sin(x))
            x          2          3                                                                                                 
                      x          x
4x2ex2−xsin⁡(x)sign⁡(sin⁡(x))+2xcos⁡2(x)δ(sin⁡(x))+2ex2+2cos⁡(x)sign⁡(sin⁡(x))−sin⁡(x)x−2cos⁡(x)x2+2sin⁡(x)x34 x^{2} e^{x^{2}} - x \sin{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} + 2 x \cos^{2}{\left(x \right)} \delta\left(\sin{\left(x \right)}\right) + 2 e^{x^{2}} + 2 \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} - \frac{\sin{\left(x \right)}}{x} - \frac{2 \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3}}
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Tercera derivada [src] 
                                                                                                         / 2\         / 2\                                                                                                   
  cos(x)   6*sin(x)                           3*sin(x)   6*cos(x)        2                            3  \x /         \x /                                  3                                                                
- ------ - -------- - 3*sign(sin(x))*sin(x) + -------- + -------- + 6*cos (x)*DiracDelta(sin(x)) + 8*x *e     + 12*x*e     - x*cos(x)*sign(sin(x)) + 2*x*cos (x)*DiracDelta(sin(x), 1) - 6*x*DiracDelta(sin(x))*cos(x)*sin(x)
    x          4                                  2          3                                                                                                                                                               
              x                                  x          x
8x3ex2+12xex2−6xsin⁡(x)cos⁡(x)δ(sin⁡(x))+2xcos⁡3(x)δ(1)(sin⁡(x))−xcos⁡(x)sign⁡(sin⁡(x))−3sin⁡(x)sign⁡(sin⁡(x))+6cos⁡2(x)δ(sin⁡(x))−cos⁡(x)x+3sin⁡(x)x2+6cos⁡(x)x3−6sin⁡(x)x48 x^{3} e^{x^{2}} + 12 x e^{x^{2}} - 6 x \sin{\left(x \right)} \cos{\left(x \right)} \delta\left(\sin{\left(x \right)}\right) + 2 x \cos^{3}{\left(x \right)} \delta^{\left( 1 \right)}\left( \sin{\left(x \right)} \right) - x \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} - 3 \sin{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} + 6 \cos^{2}{\left(x \right)} \delta\left(\sin{\left(x \right)}\right) - \frac{\cos{\left(x \right)}}{x} + \frac{3 \sin{\left(x \right)}}{x^{2}} + \frac{6 \cos{\left(x \right)}}{x^{3}} - \frac{6 \sin{\left(x \right)}}{x^{4}}
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