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Derivada de la función/ e^x^2/ (sinx)/ (x*|sinx|+e^x^2+(sinx))

Derivada de (x*|sinx|+e^x^2+(sinx))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
              / 2\         
              \x /         
x*|sin(x)| + E     + sin(x)
(ex2+x∣sin⁡(x)∣)+sin⁡(x)\left(e^{x^{2}} + x \left|{\sin{\left(x \right)}}\right|\right) + \sin{\left(x \right)} 
x*Abs(sin(x)) + E^(x^2) + sin(x)
Primera derivada [src] 
     / 2\                                            
     \x /                                            
2*x*e     + x*cos(x)*sign(sin(x)) + |sin(x)| + cos(x)
2xex2+xcos⁡(x)sign⁡(sin⁡(x))+cos⁡(x)+∣sin⁡(x)∣2 x e^{x^{2}} + x \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} + \cos{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|
Simplificar
Segunda derivada [src] 
             / 2\                                 / 2\                                                         
             \x /                              2  \x /                                  2                      
-sin(x) + 2*e     + 2*cos(x)*sign(sin(x)) + 4*x *e     - x*sign(sin(x))*sin(x) + 2*x*cos (x)*DiracDelta(sin(x))
4x2ex2−xsin⁡(x)sign⁡(sin⁡(x))+2xcos⁡2(x)δ(sin⁡(x))+2ex2−sin⁡(x)+2cos⁡(x)sign⁡(sin⁡(x))4 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}} - \sin{\left(x \right)} + 2 \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}
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Tercera derivada [src] 
                                                                       / 2\         / 2\                                                                                                   
                                       2                            3  \x /         \x /                                  3                                                                
-cos(x) - 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)
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)8 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) - \cos{\left(x \right)}
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