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x*exp(-x)exp^(((x^(2)+x)*sin(x))^(1/2))
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  • Derivada de:
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  • Expresiones idénticas

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  • x*exp(-x)exp(((x(2)+x)*sin(x))(1/2))
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  • xexp(-x)exp^(((x^(2)+x)sin(x))^(1/2))
  • xexp(-x)exp(((x(2)+x)sin(x))(1/2))
  • xexp-xexpx2+xsinx1/2
  • xexp-xexp^x^2+xsinx^1/2
  • x*exp(-x)exp^(((x^(2)+x)*sin(x))^(1 dividir por 2))
  • Expresiones semejantes

  • x*exp(x)exp^(((x^(2)+x)*sin(x))^(1/2))
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Derivada de x*exp(-x)exp^(((x^(2)+x)*sin(x))^(1/2))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
          _________________
         / / 2    \        
   -x  \/  \x  + x/*sin(x) 
x*e  *E                    
$$e^{\sqrt{\left(x^{2} + x\right) \sin{\left(x \right)}}} x e^{- x}$$
(x*exp(-x))*E^(sqrt((x^2 + x)*sin(x)))
Solución detallada
  1. Se aplica la regla de la derivada parcial:

    y .

    Para calcular :

    1. Se aplica la regla de la derivada de una multiplicación:

      ; calculamos :

      1. Según el principio, aplicamos: tenemos

      ; calculamos :

      1. Sustituimos .

      2. Derivado es.

      3. Luego se aplica una cadena de reglas. Multiplicamos por :

        1. Sustituimos .

        2. Según el principio, aplicamos: tenemos

        3. Luego se aplica una cadena de reglas. Multiplicamos por :

          1. Se aplica la regla de la derivada de una multiplicación:

            ; calculamos :

            1. diferenciamos miembro por miembro:

              1. Según el principio, aplicamos: tenemos

              2. Según el principio, aplicamos: tenemos

              Como resultado de:

            ; calculamos :

            1. La derivada del seno es igual al coseno:

            Como resultado de:

          Como resultado de la secuencia de reglas:

        Como resultado de la secuencia de reglas:

      Como resultado de:

    Para calcular :

    1. Derivado es.

    Ahora aplicamos la regla de la derivada de una divesión:

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
                                                                                                        _________________    
                                             _________________ /                   / 2    \       \    / / 2    \            
                    _________________       / / 2    \         |(1 + 2*x)*sin(x)   \x  + x/*cos(x)|  \/  \x  + x/*sin(x)   -x
                   / / 2    \           x*\/  \x  + x/*sin(x) *|---------------- + ---------------|*e                    *e  
/     -x    -x\  \/  \x  + x/*sin(x)                           \       2                  2       /                          
\- x*e   + e  /*e                     + -------------------------------------------------------------------------------------
                                                                           / 2    \                                          
                                                                           \x  + x/*sin(x)                                   
$$\frac{x \sqrt{\left(x^{2} + x\right) \sin{\left(x \right)}} \left(\frac{\left(2 x + 1\right) \sin{\left(x \right)}}{2} + \frac{\left(x^{2} + x\right) \cos{\left(x \right)}}{2}\right) e^{- x} e^{\sqrt{\left(x^{2} + x\right) \sin{\left(x \right)}}}}{\left(x^{2} + x\right) \sin{\left(x \right)}} + \left(- x e^{- x} + e^{- x}\right) e^{\sqrt{\left(x^{2} + x\right) \sin{\left(x \right)}}}$$
Segunda derivada [src]
/                                                                                                                                  __________________                                                  __________________                                      2       __________________                                                                                                                      \                          
|                                              2       __________________                                                      2*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*cos(x)   \/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))    2*\/ x*(1 + x)*sin(x) *(1 + 2*x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))                                                                      |                          
|         ((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))  + 2*\/ x*(1 + x)*sin(x) *(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x)) - ------------------------------------------------------------------- + ----------------------------------------------------------- - ----------------------------------------------------------------------     __________________                                               |    __________________    
|                                                                                                                                                             sin(x)                                                       x*(1 + x)*sin(x)                                                      x*(1 + x)                                  \/ x*(1 + x)*sin(x) *(-1 + x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))|  \/ x*(1 + x)*sin(x)   -x
|-2 + x + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------|*e                    *e  
\                                                                                                                                                                 4*(1 + x)*sin(x)                                                                                                                                                                                    x*(1 + x)*sin(x)                         /                          
$$\left(x - 2 + \frac{- \frac{2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) + \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2} - \frac{2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x \left(x + 1\right)} + \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2}}{x \left(x + 1\right) \sin{\left(x \right)}}}{4 \left(x + 1\right) \sin{\left(x \right)}} - \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x - 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x \left(x + 1\right) \sin{\left(x \right)}}\right) e^{- x} e^{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}}}$$
Tercera derivada [src]
/                                                                                                                                                                                                                                                                                          2              __________________                                             __________________                                                                                                    2                                                    3       __________________    2                                              __________________                                      3     __________________                                      3       __________________                                                                    __________________          2                                             __________________                                      2              __________________                                      2                 __________________                                                                                                __________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \                          
|              __________________                                                           __________________                                                                                                                                      6*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) *cos(x)   8*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))   8*\/ x*(1 + x)*sin(x) *(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x))*cos(x)   6*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) *(1 + 2*x)   3*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))    8*\/ x*(1 + x)*sin(x) *cos (x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))   \/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))    \/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))    8*\/ x*(1 + x)*sin(x) *(1 + 2*x)*(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x))   8*\/ x*(1 + x)*sin(x) *(1 + 2*x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))   6*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) *cos(x)   6*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) *(1 + 2*x)   6*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x))   8*\/ x*(1 + x)*sin(x) *(1 + 2*x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*cos(x)              /                                                                                                                         __________________                                                  __________________                                      2       __________________                                                \                                                                        |                          
|        - 4*\/ x*(1 + x)*sin(x) *(-6*cos(x) + 3*(1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) + 4*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x)) + 6*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x)) - ----------------------------------------------- - ------------------------------------------------------------ - -------------------------------------------------------------------------------- - -------------------------------------------------- + ---------------------------------------- + -------------------------------------------------------------------- + ----------------------------------------------------------- + ----------------------------------------------------------- - ----------------------------------------------------------------------------------- + ----------------------------------------------------------------------- - -------------------------------------------------------------------- - ----------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------              |                                     2       __________________                                                      2*\/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))*cos(x)   \/ x*(1 + x)*sin(x) *((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))    2*\/ x*(1 + x)*sin(x) *(1 + 2*x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))|                                                                        |                          
|                                                                                                                                                                                                                                                                        sin(x)                                                x*(1 + x)                                                                  sin(x)                                                            x*(1 + x)                                    x*(1 + x)*sin(x)                                                2                                                           x*(1 + x)*sin(x)                                             2        2    2                                                               x*(1 + x)                                                                       2        2                                                                       2                                                            2        2                                                                                    x*(1 + x)*sin(x)                                                                                 x*(1 + x)*sin(x)                                 3*(-1 + x)*|((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))  + 2*\/ x*(1 + x)*sin(x) *(2*sin(x) + 2*(1 + 2*x)*cos(x) - x*(1 + x)*sin(x)) - ------------------------------------------------------------------- + ----------------------------------------------------------- - ----------------------------------------------------------------------|       __________________                                               |    __________________    
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     sin (x)                                                                                                                    x *(1 + x) *sin (x)                                                                                                                                           x *(1 + x)                                                           x*(1 + x)*sin (x)                                                        x *(1 + x) *sin(x)                                                                                                                                                                                                                                          \                                                                                                                                                    sin(x)                                                       x*(1 + x)*sin(x)                                                      x*(1 + x)                               /   3*\/ x*(1 + x)*sin(x) *(-2 + x)*((1 + 2*x)*sin(x) + x*(1 + x)*cos(x))|  \/ x*(1 + x)*sin(x)   -x
|3 - x + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------|*e                    *e  
\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 8*(1 + x)*sin(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         4*x*(1 + x)*sin(x)                                                                                                                                                                                          2*x*(1 + x)*sin(x)                         /                          
$$\left(- x + 3 + \frac{4 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) + \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - 4 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + 3 \left(2 x + 1\right) \sin{\left(x \right)} - 6 \cos{\left(x \right)}\right) - \frac{6 \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + 6 \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) + \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \left(x + 1\right) \sin{\left(x \right)}} - \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)}{x \left(x + 1\right)} + \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{3}}{x \left(x + 1\right) \sin{\left(x \right)}} - \frac{6 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2} \cos{\left(x \right)}}{x \left(x + 1\right) \sin^{2}{\left(x \right)}} + \frac{6 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)}{x \left(x + 1\right) \sin{\left(x \right)}} - \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x \left(x + 1\right)} - \frac{6 \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2}}{x \left(x + 1\right)} + \frac{3 \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{3}}{x \left(x + 1\right) \sin{\left(x \right)}} + \frac{8 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right)^{2} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x^{2} \left(x + 1\right)^{2}} - \frac{6 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2}}{x^{2} \left(x + 1\right)^{2} \sin{\left(x \right)}} + \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{3}}{x^{2} \left(x + 1\right)^{2} \sin^{2}{\left(x \right)}}}{8 \left(x + 1\right) \sin{\left(x \right)}} + \frac{3 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x - 2\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{2 x \left(x + 1\right) \sin{\left(x \right)}} - \frac{3 \left(x - 1\right) \left(- \frac{2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(- x \left(x + 1\right) \sin{\left(x \right)} + 2 \left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) + \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2} - \frac{2 \sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(2 x + 1\right) \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)}{x \left(x + 1\right)} + \frac{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}} \left(x \left(x + 1\right) \cos{\left(x \right)} + \left(2 x + 1\right) \sin{\left(x \right)}\right)^{2}}{x \left(x + 1\right) \sin{\left(x \right)}}\right)}{4 x \left(x + 1\right) \sin{\left(x \right)}}\right) e^{- x} e^{\sqrt{x \left(x + 1\right) \sin{\left(x \right)}}}$$
Gráfico
Derivada de x*exp(-x)exp^(((x^(2)+x)*sin(x))^(1/2))