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x*exp(-x)x*arctg√(2x-1)-(√(2x-1))/2
Derivada de la función/ x*exp(-x)x*arctg√(2x-1)-(√(2x-1))/2

Derivada de x*exp(-x)x*arctg√(2x-1)-(√(2x-1))/2

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

Gráfico:

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Solución

Ha introducido [src] 
                              _________
   -x       /  _________\   \/ 2*x - 1 
x*e  *x*atan\\/ 2*x - 1 / - -----------
                                 2
xxe−xatan⁡(2x−1)−2x−12x x e^{- x} \operatorname{atan}{\left(\sqrt{2 x - 1} \right)} - \frac{\sqrt{2 x - 1}}{2} 
((x*exp(-x))*x)*atan(sqrt(2*x - 1)) - sqrt(2*x - 1)/2
Gráfica
02468-8-6-4-2-10105-5
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Primera derivada [src] 
                                                                         -x    
        1         /  /     -x    -x\      -x\     /  _________\       x*e      
- ------------- + \x*\- x*e   + e  / + x*e  /*atan\\/ 2*x - 1 / + -------------
      _________                                                       _________
  2*\/ 2*x - 1                                                    2*\/ 2*x - 1
xe−x22x−1+(x(−xe−x+e−x)+xe−x)atan⁡(2x−1)−122x−1\frac{x e^{- x}}{2 \sqrt{2 x - 1}} + \left(x \left(- x e^{- x} + e^{- x}\right) + x e^{- x}\right) \operatorname{atan}{\left(\sqrt{2 x - 1} \right)} - \frac{1}{2 \sqrt{2 x - 1}}
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Segunda derivada [src] 
                        -x                                                                 -x               -x                   -x 
       1               e                                      /  __________\  -x        x*e              x*e           (-2 + x)*e   
--------------- + -------------- + (2 - 2*x + x*(-2 + x))*atan\\/ -1 + 2*x /*e   - --------------- - -------------- - --------------
            3/2       __________                                                               3/2       __________       __________
2*(-1 + 2*x)      2*\/ -1 + 2*x                                                    2*(-1 + 2*x)      2*\/ -1 + 2*x    2*\/ -1 + 2*x
−xe−x22x−1−xe−x2(2x−1)32−(x−2)e−x22x−1+(x(x−2)−2x+2)e−xatan⁡(2x−1)+e−x22x−1+12(2x−1)32- \frac{x e^{- x}}{2 \sqrt{2 x - 1}} - \frac{x e^{- x}}{2 \left(2 x - 1\right)^{\frac{3}{2}}} - \frac{\left(x - 2\right) e^{- x}}{2 \sqrt{2 x - 1}} + \left(x \left(x - 2\right) - 2 x + 2\right) e^{- x} \operatorname{atan}{\left(\sqrt{2 x - 1} \right)} + \frac{e^{- x}}{2 \sqrt{2 x - 1}} + \frac{1}{2 \left(2 x - 1\right)^{\frac{3}{2}}}
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Tercera derivada [src] 
                          -x             -x               -x              -x                    -x                                                             -x                               -x               -x  
         3               e              e              x*e             x*e            (-2 + x)*e                                 /  __________\  -x       3*x*e         (2 - 2*x + x*(-2 + x))*e       (-2 + x)*e    
- --------------- - ------------- - ------------ + ------------- + -------------- + --------------- - (6 - 3*x + x*(-3 + x))*atan\\/ -1 + 2*x /*e   + --------------- + -------------------------- + ----------------
              5/2             3/2     __________             3/2       __________               3/2                                                               5/2             __________               __________
  2*(-1 + 2*x)      (-1 + 2*x)      \/ -1 + 2*x    (-1 + 2*x)      2*\/ -1 + 2*x    2*(-1 + 2*x)                                                      2*(-1 + 2*x)            x*\/ -1 + 2*x          2*x*\/ -1 + 2*x
xe−x22x−1+xe−x(2x−1)32+3xe−x2(2x−1)52+(x−2)e−x2(2x−1)32−(x(x−3)−3x+6)e−xatan⁡(2x−1)−e−x2x−1−e−x(2x−1)32−32(2x−1)52+(x−2)e−x2x2x−1+(x(x−2)−2x+2)e−xx2x−1\frac{x e^{- x}}{2 \sqrt{2 x - 1}} + \frac{x e^{- x}}{\left(2 x - 1\right)^{\frac{3}{2}}} + \frac{3 x e^{- x}}{2 \left(2 x - 1\right)^{\frac{5}{2}}} + \frac{\left(x - 2\right) e^{- x}}{2 \left(2 x - 1\right)^{\frac{3}{2}}} - \left(x \left(x - 3\right) - 3 x + 6\right) e^{- x} \operatorname{atan}{\left(\sqrt{2 x - 1} \right)} - \frac{e^{- x}}{\sqrt{2 x - 1}} - \frac{e^{- x}}{\left(2 x - 1\right)^{\frac{3}{2}}} - \frac{3}{2 \left(2 x - 1\right)^{\frac{5}{2}}} + \frac{\left(x - 2\right) e^{- x}}{2 x \sqrt{2 x - 1}} + \frac{\left(x \left(x - 2\right) - 2 x + 2\right) e^{- x}}{x \sqrt{2 x - 1}}
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Gráfico
Derivada de x*exp(-x)x*arctg√(2x-1)-(√(2x-1))/2
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